High above the world of humans, beyond the burning rainbow bridge, lies Asgard – the fortified home of the Æsir. It is fortress, city and heaven all at once: a place of golden halls, ringed by a wall that holds one of the cunningest stories of the North.
Asgard (Old Norse Ásgarðr, „enclosure of the Æsir“) is joined to the other worlds through the world-tree Yggdrasil. At its centre lies the field Idavöll, where the gods build their hall, play with golden game-pieces and hold court. From here Odin surveys all nine worlds from his high seat Hlidskjálf.
Asgard is rich in halls: Valhalla, where Odin gathers the fallen warriors; Breidablik, the purest hall of Balder; Fensalir of Frigg; Thrúdheim/Bilskirnir, the huge hall of Thor with its supposed 540 rooms; Himinbjörg, where Heimdall guards the bridge; and Fólkvangr, the realm of Freyja, who likewise receives a share of the fallen.
The most famous Asgard story is the building of its protective wall. A stranger, a master-builder, offers to raise an impregnable wall in a single winter – in payment he demands the sun, the moon and the goddess Freyja. On Loki's advice the gods accept, certain he will fail. But the builder has a magic stallion, Svaðilfari, who hauls immense stones night after night – and the wall grows dangerously fast.
To save the wager, Loki turns himself into a mare and lures the stallion away. Without his draught-horse the builder misses the deadline; he reveals himself as a giant and is slain by Thor. Loki, though, later gives birth to the eight-legged steed Sleipnir, swiftest of all horses – Odin's mount. So out of a deceit comes a treasure.

Valhalla · Bifröst · The nine worlds · Odin & Sleipnir · Loki · Hlidskjálf & the treasures.
Poetic Edda: Völuspá (Idavöll), Grímnismál (the halls). Snorri Sturluson, Prose Edda (Gylfaginning: Asgard, Hlidskjálf, the wall-building; Prologue: the Troy equation), c. 1220. German public-domain translation: Karl Simrock, Die Edda (1851). Scholarship: Rudolf Simek, Dictionary of Northern Mythology; John Lindow, Norse Mythology (2001).