The map runs to sixteen laminated foolscap pages, or about ten square feet, when I tile the pages together. I have been given it on the condition that I do not pass it on. It is not like any map I have ever seen, and I have seen some strange maps in my time. The plan of the above-ground city is traced carefully in pale silver-gray ink, such that, if you read only for the gray, you can discern the faint footprints of apartment blocks and embassies, parks and ornamental gardens, boulevards and streets, the churches, the railway lines and the train stations, all hovering there, intricate and immaterial.

The map’s real content—the topography it inks in black and blue and orange and red—is the invisible city, the realm out of which, over centuries, the upper city has been hewn and drawn, block by block. This invisible city follows different laws of planning to its surface counterpart. Its tunnelled streets often kink and wriggle, or run to dead ends. Some of them curl back on themselves like whips. At junctions, three or four tunnel-streets might spray out. There are slender highways running almost the length of the tiled map, from southwest to northeast. There are inexplicably broken grids of streets, or hubs where the spokes of different tunnels meet. Coming off some of the tunnels are chambers, irregular in their outlines and with dozens of small connecting rooms.

The map’s place names traverse a range of cultural registers, from the classical to the surreal to the military-industrial. The Room of Cubes. The Boutique of Psychosis. Crossroads of the Dead. The Medusa. Bunker Under the Mountain. The Monastery of the Bears. Ossa Arida. Room Z. Affordance is specified on the map in handwritten cursive words: “Low,” “Quite low,” “Very low,” “Tight,” “Flooded,” “Impracticable,” “Impassable.” More detail is occasionally given: “Humid and unstable region (sometimes flooded)”; “Beautiful gallery, vaulted and corbelled.” “Chatières”—cat-flaps—mark a point of lateral transition between tunnel and tunnel, or between tunnel and chamber. Other captions gloss contact sites between the upper city and the invisible city (“Hole to the sky”) or between levels (“Tiny hole in the ground debouching into a dangerous lower level”). Scattered around the map are little inked skulls-and-crossbones and laconic warnings of danger: “Cave-in”; “Open well: dangerous”; “Collapsing ceiling.”

Here and there, boxed-out cartouches offer stories of individual sites. A blue compass rose with an orange northward arrow is laid over an empty section of each page, and each page is given a district name. The typeface is a fine, seriffed font that I do not recognize. The over-all aesthetic is coolly contemporary, the cartography itself an elegant compression. Authorship is attributed only to a collective called Nexus—“the connection or connections between the parts of a system or a group of entities.” I admire the work of its anonymous makers.

On the day we first go down into the invisible city, castle clouds mass over the lowlands to the north of our entrance point. Flat fields, square-steepled church towers, lines of poplars, red-tiled farms. My last sight of the sun is a westerly blaze under rain clouds. At dusk, we push through a door in a wall marked “Interdit d’entrer,” slip through a hole in a chain-link fence, scramble down to a railway line, and crunch along the tracks toward the brick arch of a tunnel. The cutting banks are tangled with acacia trees and wild clematis. Apartment blocks rise above the cutting on both sides. Once in the railway tunnel, we keep between the tracks, because what little light there is glints on the metal and shows us the way.

Ahead, in the darkness, is a flock of fireflies: soft orange lights bobbing in the black air. We draw closer, and bodies gradually attach themselves to the lights, which are the bared flames of carbide lamps mounted on people milling around one side of the tunnel. They are standing around, smoking and talking, carbide cannisters belted at their waists, with pipes leading up to burners strapped to their heads. From the burners hiss the two horns of orange flame, low in temperature but high in luminosity. They nod greetings to us, murmuring in French and English. Down at track level, where one side of the tunnel begins to rise, is a ragged hole in the ground, just wide enough to admit a person. A few yards to its right, I can see the outline of what had once been a similar hole, now plugged with fresh-looking concrete.

I have come to the catacombs with two friends—let us call them Lina and Jay. Jay is a caver keen to extend his explorations into city systems. He is droll, unflappable, and strong. Lina is the leader of our group, and she has been here many times. She is passionate about the catacombs, especially about preserving and documenting their swiftly changing features through photography and record-keeping. She wears bright lipstick, and she ties her curly brown hair back to keep it out of trouble in the tunnels. Below ground, she is calm and cool in her decision-making, warm and generous with her knowledge and her sharing of this space. Without Lina’s trust, I wouldn’t be able to access the “network,” as she refers to it. I feel fortunate to be with her.

“The cataflics came down and filled that one up,” Lina says, pointing to the plugged hole at track level. “So the cataphiles lit a fire to soften the stone and then used pickaxes to open up this new one. It’s probably the safest way in and out right now, but we’ll plan to exit by a manhole, whenever we come out.” She gestures back up the tunnel with a smile, then eases herself feet first into the ragged hole, raises her arms above her head, and disappears.

All cities are additions to a landscape that require subtraction from elsewhere. Much of Paris was built from its own underland, hewn block by block from the bedrock and hauled up for dressing and placing. Underground stone quarrying began in the thirteenth century, and Lutetian limestone was used in the construction of such iconic buildings as Notre-Dame Cathedral, the Louvre, and Saint-Eustache Church. The result of more than six hundred years of quarrying is that beneath the southern portion of the upper city exists its negative image: a network of more than two hundred miles of galleries, rooms and chambers, extending beneath several arrondissements. This network is the vides de carrières—the quarry voids, the catacombs, which together total an underground space around ten times the space of Central Park.

Quarrying techniques changed surprisingly little over time. Shafts were driven sixty feet or so down to the limestone layers, then tunnels were cut laterally from there, following the strata. Where larger rooms were excavated, pillars of stone were left unquarried to support the ceilings. The standard tunnel was cut to six feet high and three feet wide: enough to accommodate a man pushing a barrow filled with stone. Dynasties of quarrymen came and went, passing down skills from father to son, extending the maze.

For centuries, quarrying was ill-regulated and largely unmapped. Then, in the mid-eighteenth century, the extensive undermining began to have consequences for the upper city, causing subsidence sinkholes, known as fontis, that were reputed to be of diabolic origin. The quarry voids had begun to migrate to the surface; the under city had begun to consume its twin. In 1774, a fonti engulfed, in a matter of seconds, pavements, houses, horses, carts, and people. The site of the sinkhole was, of all places, the Rue d’Enfer—the Street of Hell. Several minor cave-ins followed, and panic spread in the city at the unknown extent of the invisible danger.

Louis XVI responded, shortly after his accession, by creating an inspection unit for the “Quarries Below Paris and Surrounding Plains,” headed by a general inspector named Charles-Axel Guillaumot, and tasked with regulating the quarries for the purposes of public safety. It was Guillaumot who initiated the first mapping of the void network, with a view to consolidating exie in 1793, and his body was not discovered until eleven years later. As such, he was arguably the world’s first, and one of its worst, urban explorers.

For some years before coming to the catacombs, I had been finding my way into the subculture of urban exploration, an activity that might best be defined as exploratory trespassing in the built environment: adventuring into storm-drain and sewer networks; topping out bridges, construction cranes, and skyscrapers; and accessing former military installations, disused hospitals, and other ruined or abandoned sites. Urban exploration is international in its geography, with groups, crews, and chapters scattered around the world. There is a surprising number of female explorers, and the class base is mixed, often drawing on a disaffected and legally disobedient demographic. At its more political fringes, urban exploration mandates itself as a radical act of disobedience and liberation, a protest against state constraints on freedom within the city. The subculture has its subcultures: there are explorers who specialize in “track-running” underground rail systems to gain access to off-limits parts of those networks; others are particularly known for their ascents of factory chimneys in former Soviet-bloc countries. Detroit and Pripyat—the city evacuated after the Chernobyl disaster—might be thought of as two meccas for those urban explorers who seek out the problematic pathos of “derp” (explorers’ argot for “derelict and ruined places”), Instagramming shots of collapsing pianos, scattered archives, and children’s toys abandoned in the corners of dusty rooms.

There are aspects of urban exploration that leave me deeply uneasy, and that cannot be fended off by indemnifying gestures of self-awareness on the part of its practitioners. I dislike its intermittent air of hipster entitlement and its inattention toward those people whose working lives involve the construction, operation, and maintenance—rather than the exploration—of these hidden structures of the city. Other aspects of the subculture have come to compel me, though, and so I began—cautiously—to spend increasing amounts of time with those who identified as explorers, and whose styles of pursuing their passion I admired.

Lina’s great wish as an explorer is to enter the Odessa catacombs. Odessa, like Paris, is a city built on limestone, and it contains the world’s most extensive sub-urban quarries. Some fifteen hundred miles of tunnel make up Odessa’s invisible city, sinking to a depth of a hundred and sixty feet over three levels. When the Germans were closing in on Odessa during the Second World War, the Soviets left Ukrainian partisan groups hidden in the catacombs; down in the dark, they established kitchens, shooting ranges, dormitories, and armories. Cat-and-mouse games were played between occupiers and the rebel groups; the Germans gassed and bombed the tunnel systems in an attempt to kill the Russians. After the war in Odessa, the underworld moved into this underland, and smugglers and criminals enlarged the network for their own purposes.

“The Odessa tunnels make ours here in Paris look like a sideshow,” Lina says that afternoon, in the catacombs. “But it’s dangerous there. Especially for a woman. Bad stories circulate about what can happen there, about what has happened. Definitely murders. Probably at least one death through simply getting lost.”

The approach to the Salle du Drapeau—the Room of the Flag—is the only time when I feel real fear in the Parisian catacombs. It is early evening in the upper city by the time we get close to the room. On the surface, people are leaving offices, walking home through dusk streets, boarding trains and buses, stopping for drinks in bars.

Down in the invisible city, we are heading northwest along a tunnel with no side turnings, the ceiling of which is dropping steadily lower. I walk with a bent neck, then with hunched shoulders; then I have to lean at the waist, and then, at last, I have to drop to my knees and can only crawl forward.

Ahead of me, past Lina, the tunnel seems to cinch to a dead end. I wait for Lina to admit that she has at last led us the wrong way. Lina says nothing. The yellow of the limestone ahead glows in her torchlight. She shrugs off her pack, pushes it behind her, loops one of its straps around one of her ankles, and then eases herself head first into what I can now see is a tiny floor-level opening, perhaps eighteen inches high, where I thought the tunnel ended. My heart shivers fast, and my mouth dries up instantly. My body does not want to enter that opening.

“You’ll need to pull your pack along with your toes here,” Lina says. Her voice is muffled. “And from now on don’t shout or touch the ceiling.”

Fear slithers up my spine, spills greasily down my throat. Nothing to do but follow. I lie flat, loop pack to foot, edge in head first. The clearance above is so tight that again I have to turn my skull sideways to proceed. The clearance to the sides is so scant that my arms are nearly locked to my body. The stone of the ceiling is cracked into blocks, and it sags around the cracks. Claustrophobia suddenly grips my full body like a vice, pressing in on my chest and lungs, squeezing my breath hard, setting black stars exploding in my head.

There’s the drag-scratch of my bag behind me, pain already in the leg to which it is looped, from the effort of pulling it. Movement is a few inches at a time, a snakelike wriggle, gaining purchase with shoulders and fingertips. How long does this tunnel run like this? If it dips even two inches, I’ll be stuck. The thought of continuing is atrocious. The thought of reversing is even worse. Then the top of my head bumps against something soft.

Ahead I can just see, by cocking my neck back, that the underside of Lina’s rucksack is jammed against the dipping edge of a block in the ceiling. The pack is jerking around, trying to get free; she must be hauling at it with her leg, but it looks as if it could loosen the block at any moment and bring the ceiling down.

“Easy, easy!” I shout and she shouts back, telling me not to shout. Pop—and the bag comes free, slithers on.

I shuffle forward toward the pinch when suddenly—what the fuck?—I can feel the stone around me, the stone that encases me, the stone that is measuring me up like a coffin, start to vibrate. A faint shudder at first, but clear and now growing in strength and noise. The ceiling, the unstable ceiling, is humming with tremors. The vibrations are passing through the stone and my body, then on into the stone beneath me. The rumbling rises to a thunder, and I can hear clacks and clicks among the rumblings, and I remember the spectre architecture, the faint gray outline of the upper city on this page of the map: train lines arcing in, joining like tendons and running together into Montparnasse station.

These are trains above us; we are directly underneath the Métro and over-ground lines, and it is decades of train judder that has left the ceiling unstable here. I want to shout but mustn’t, want to retreat but can’t, so I just keep inching forward, stone dust in my mouth, finger-scrabble against the rough rock, hauling the bag behind me, all in silence—just the rumble of the trains rising and falling away, my heaving breath, and my drumming heart. And then, after a few minutes of that sick-making fear, the space widens and lifts, and then we can kneel again, and then we can stand, and then we can walk, and then we are close to the Salle du Drapeau.

A flooded tunnel leads toward a chamber. Orange light on the water, washing and rocking, although the water itself is still. Cries come from through the doorway, and there is the sound of music: The Jam’s “Going Underground,” growing in volume, booming down the tunnel. I smile in recognition of the music, bridge onto ledges on either side of the flooded tunnel, and reach the doorway. It opens into a high-sided room, the roof twenty feet or more above us. The space above makes my head feel as if it is helium-filled, floating. A big tricolor flag is painted high on one of the walls. And there are people standing up to greet us: embraces for Lina, shakes of the hand for me and Jay, welcoming smiles for us all.

We have found our way to a wunderkammer, filled with music and hospitality. There is a table spread with food and drink: fruit, baguettes, wheels of brie and camembert, bottles of spirits, cans of beer. A boxy CD player sits in the middle of the table, wired up to two small speakers.

The Jam changes to Bowie’s “Underground.”

“Ça c’est le cataboum!” one of the strangers says, pointing at the music box, nodding in time to the beat.

White fairy-lights are strung around the room. It is all deeply surreal—as if we have stumbled into a postmodern mead hall, far underground. A plastic glass of vodka is pressed into my hand, and I knock it back gratefully. It burns in my belly, and my time in the train rift instantly softens around its edges. My glass is refilled with brown rum from a label-less bottle. I catch myself grinning. I feel grateful for this place, for the juxtapositions of the catacombs, tilting from terror to warmth in the twist of a tunnel.

Introductions are made. There are two French cataphiles who go by handles I do not catch, and a Canadian named T, who is an old friend of Lina’s, and who works as an au pair during the day and comes down into the catacombs often at night. All three are wearing Indiana Jones-style leather hats, and one of the Frenchmen has brought a whip and a three-foot-long taper made of a wooden broom handle and wax-soaked strips of denim torn from a pair of jeans.

Bowie changes to “Underground” by Ben Folds Five. Everyone cheers.

We eat more, drink more, talk more. Hours pass. I mostly listen, relaxing after the day’s exertions, pinching myself at the wondrously weird subcultures of this underland, reflecting on the bizarre cultural recyclings that it calls out.

Much later, Lina, Jay, and I set off to find a sleeping place. We reach a zone called the Air-Raid Shelters. A wide tunnel avenue is lined with a series of hooped semicircular chambers with reinforced ceilings. They are of Second World War origin, Lina says, shelters adapted to resist bomb fall. Now they make ideal dormitories for tired cataphiles. There, with a shelter chamber each to ourselves, we settle down. The distant passage of trains vibrates the walls.

The next day we ready to leave the invisible city. The original plan was to exit by means of a laddered manhole that Lina has been told is presently unwelded. Its nickname is the Chatière of Death, which doesn’t endear it to me. But the directions Lina has received as to its whereabouts are vague, and we can’t locate it.

So we return to our point of entry. We endure hours of tiring travel through tunnels from the far northwest of the system. Lina plots a long way around that circumvents the crawl space leading to the Salle du Drapeau. We see no one else in the course of our traverse. Once we pass a stretch of tunnel wall on which I see hand stencils that have been made with spray cans in acid green, ice blue, nuclear yellow, punk echoes of prehistoric cave art. We come back through the Carrefour des Morts and back at last down Banga, in which the water level has risen noticeably since we first crossed it days earlier.

“It must have been raining up there,” Lina says.

We reach the access hole and climb, one by one, up and out into the train tunnel. After our days of confinement, its ceiling seems as huge as a ballroom. Away to our left is a familiar arch of light. We crunch back down the railway track, and the upper world moves into view. A pigeon glides, stiff-winged, across the arch-framed sky. Steep sides of the cutting show themselves, acacia branches leaning in from the banks to drop their butterfly leaves.

We stop at the point where the light meets the shadow, look up, and there is the impossible sun. We speak quietly to one another. Our hair is pomaded with sweat and stone dust. The air smells of cucumber and smoke. In one of the apartments high above us, a woman is hanging white sheets on the balcony.

We walk on, scrambling up the cutting side, through the hole in the chain-link fence, out by the doorway marked “Interdit d’entrer.” On a street corner three turns from the doorway, a woman stops us to ask if we have come from “en bas,” from “underneath.” Yes, we say, we have.

This essay is adapted from “Underland: A Deep Time Journey,” published by Hamish Hamilton and W. W. Norton & Company.