In September 1842 the Antarctic explorer Charles Wilkes was court-martialed on a charge of "immoral mapping". Two years earlier Wilkes had claimed to have sighted the coast of a "vast Antarctic continent", visible across an "impenetrable barrier of ice". He had modestly named his discovery "Wilkes Land", mapped it and reported his find to the Secretary of the American Navy. But the following year the English explorer James Ross falsified Wilkes's claim, dismissing Wilkes Land as "a pseudo-continent"  and so Wilkes was hauled into court on suspicion of cartographical deceit.

It is now thought likely that Wilkes had in fact himself been deceived, the victim of a mirage bred by cloud vapour and refracted light, peculiar to the trickster optics of the Antarctic. Mirages are not the same as illusions: they are, as it were, real hallucinations  authentic experiences of the eye.Wilkes had seen a cloud-mass which impeccably mimicked a land-mass, and in that sense his map had told the truth.

The history of cartography is littered with such pseudo-continents, chimerical islands, dream-rivers and other Wilkean visions, flickering between the literal and the mythical. This is partly because cartographers have often tended also to be dreamers, seduced into their science by the beauty of maps and the flights of imagination that they prompt. Maps seek to mark the world and fix its flux, but in doing so they also loosen it from its moorings: as documents, they are at once fiercely empirical and faintly mystical.

Judith Schalansky was a map-dreamer from a young age. Born in East Germany in 1980, unable to journey far because of state restrictions, she became "a child of the atlas". By the time the Berlin wall fell she had "already grown used to travelling through the atlas by finger . . . conquering distant worlds in my parents' sitting room". Imaginary voyages continued to substitute for real ones. She became especially fascinated by the world's most isolated islands and their prisoners, castaways, natives and colonists. Content to explore these territories remotely through document and image, rather than through physical visits, Schalansky conceived of a book that would pay homage to her islands of the mind  her archive-archipelago. Like the hero of Joris-Karl Huysmann's novel A Rebours, who sets off for London from Paris but realises he need go no further than the Gare du Nord, she decided to make a virtue of absence. The result is what must be the first ever atlas produced by sitting still.

Schalansky studied as an art historian, trained as a graphic designer and is also a typographer (Fraktur Mon Amour is a book-length love-letter to a single font), and this unusual skill-set has been brought brilliantly to bear on her Atlas (translated by Christine Lo). The German Arts Foundation sponsors a prize which simply rewards "the most beautiful book of the year"; it is hard to imagine that the Atlas was run close for the prize when it won in 2009. It is an utterly exquisite object: atlas as Wunderkammer and bestiary, bound in black cloth and sea-blue card, its fore-edge bright orange, and its pages populated by rare creatures and lost explorers.

Each of the 50 islands has a double-page devoted to it. Each left-hand page gives the island's global grid reference, size, name, national "owner", its distance from other islands and coasts, plus a timeline of its discovery and incidents in its history. Beneath these data comes a semi-fictional paragraph, close to prose-poem, that tells a scene from that island's past. Few of these stories are paradisal. The insularity of islands has frequently magnified emotion until it combusts: Schalansky writes of cannibalism, rape and human-rights abuses, of atom bomb tests and ecological catastrophes. "Human beings travelling far and wide," she notes quietly, "have turned into the very monsters they chased off the map." On each right-hand page is a map of the island in question, usually set in an expanse of grey-blue sea. The land is subtly rendered in greyscale and white: these islands hang like ghosts or moons in their waters. The landforms themselves are delicately drawn in plan-view, the ground intricately dot-marked to indicate low contours, and with moiré ripples showing summits and steeper slopes. Spot heights are noted, there is the occasional toponym ("Misery-Fjellet", "Deadwood Plain"). Otherwise deprived of context, the islands stand as spectres; poised  like Wilkes Land  somewhere between the actual and the visionary.

In her foreword, Schalansky describes the act of finger-walking a map as an "erotic gesture". Cartophiles will know instantly what she means: not that there is a sexual frisson involved in map-reading, but that the distant longing for a landscape is usually far greater than the satisfaction gained by reaching it (eroticism's essence being anticipation rather than consummation). "There is no more poetic book than an atlas," Schalansky writes, and her book makes a magnificent case for the atlas to be recognised as literature, worthy of its original name  theatrum orbis terrarum, "the theatre of the world".

Infinite City, Rebecca Solnit's differently extraordinary work, tips its hat to Italo Calvino's Invisible Cities , and there is plenty of Calvino's whimsical cosmi-comedy to be found here. Its subtitle is (and I offer a heavily abridged version): "A San Francisco Atlas of Principal Landmarks and Treasures of the Region, Including Butterfly Species, Queer Sites, Murders, Coffee, Water, Power, Contingent Identities  and other Significant Phenomena, Vanished and Extant". What Solnit, like Borges, well knows is that the science of cartography is limited: no map can hope to represent all aspects of any site, however small. "What we call places are stable locations with unstable converging forces," she writes in her opening essay, and so her atlas records a vision of San Francisco as utterly specific but also involved with wider networks and flows (of capital, species, migration, language). It seeks to represent both the city's quiddity and its liquidity.

Infinite City has been more than four years in the making. The book bears Solnit's name and was her idea, but is warmly acknowledged to be the work of a cooperative of artists, writers, historians, researchers and cartographers from the Bay Area, all of whom have laboured together to produce this complex valentine to a complex place. It takes the form of 22 inventive maps of San Francisco and its environs, each with an accompanying essay. Those familiar with Solnit's astonishingly varied career as activist, writer, essayist, urbanist, historian and landscape aesthetician will be unsurprised at this latest generic twist. Solnit followers will also recognise some of this atlas's preoccupations (Eadward Muybridge; the military-industrial complex's relationship with ecology; gender and landscape) and its progressive politics (she sees San Francisco as "the most left part of the left coast, the un-American place where America invents itself"). Since 1990 Solnit has published 12 books, dissimilar in mode but united by her argumentative fire and her elegance as a stylist. There is no one quite like her at work in this country, and I wish there were.

The maps that her atlas comprises are various in style. A baroque map  with inset cartouches, elaborate borders and corner curlicues  plots the activities of San Francisco's "Green Women", who battled to preserve parks and green space as the city grew rapidly in the 20th century. Another, taking its design cue from tattoo art, represents "The Bay Area As Conservative/Military Brain Trust" and locates the Northrop Grumman missile-component company, Travis Air Force Base and the Chevron refinery ("where Iraqi crude oil is refined").

My favourite map, called "Monarchs and Queens", colourfully co-maps "Butterfly Habitats and Queer Public Spaces" in the city. Painted Ladies and painted ladies dance gaily in its margins (though there is, it is worth noting, no overlap of habitat between San Francisco's gay culture and its butterflies, except that the Western Tiger Swallowtail occasionally strays near to the Ramrod, the Stud, Toolbox and Mona's Barrel House). Its closest map-relative is the wonderful "Dharma Wheels and Fish Ladders", which plots the routes of salmon migrations up the Bay Area rivers alongside the spread of Soto Zen Buddhism in the region.

The last map of Infinite City looks soberingly to the future, offering a vision of what San Francisco might resemble in 2100, after climate change has led to a sea-level rise of a metre and a half. The Embarcadero is flooded, Mission Bay is tidal salt marsh, Bayshore Boulevard is lapped at by the ocean  and the city itself has become almost a remote island.

Robert Macfarlane's The Wild Places is published by Granta.