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.