Since this volume collects all of Borges' originally independent collections, I'll give each its own space here, as I read them: 
 A Universal History of Iniquity (1935): A series of short bio-pics -- artistically licensed (and sometimes dubiously accurate) recreations of historical lives and legends. Borges himself, in his introduction, characterizes them as the work of a writer incapable of writing outright fiction of his own (despite, in characteristic contradiction, the inclusion of one traditional short story afterall). Nothing particularly groundbreaking, but a good introduction to a lot Borges' tendencies: his conflations of real and imagined, his manipulated historical references and bibliographies, and his invocations of mythologized magic. 
 The Garden of Forking Paths (1941): Though it would later become the first half of the classic Ficciones, The Garden of Forking Paths was originally published independently, and sees the foundations laid by Borges' earlier collection spawning not only the palatial mass of his imagination, but endless spires, parapets and bridges springing upwards to be lost in the sun. Unsurprisingly, the collection is filled with fabricated publications. Where before Borges had modified actual stories he had read to suit his needs, here he has generated entire fictional bodies of work, finding it simpler and more direct to write literary criticism of notional books than to write the books themselves. The best, however, may the purely fantastic constructions: "Circular Ruins" and its contemplation of creativity and subjective reality, "The Lottery in Babylon" and its microcosm of universal mysteries of causality, and, best of all, "The Library of Babel", the infinity and chaos of the universe made slightly more manageable by reducing it to a precisely defined set: an endless library and its endless books. Dazzling, and perhaps still unmatched in fiction in their elegant reductions of huge and unwieldy conceptual problems. 
 Artifices (1944): The second half of Ficciones proceeds with a similar flair to the first, though with less of the cryptic, conceptual mythologizing of "The Library of Babel" and "The Lottery in Babylon" and more pseudo-scholarly discourse (along with the usual mystery stories and Uruguayan frontier tales). For a return to the full consuming brilliance of those former works, we must continue to... 
 The Aleph (1949): ...which opens with another instant favorite, "The Immortal", which both reveals Borges to be none other than Homer himself, while out Lovecrafting Lovecraft's horrible, maddening architectures and geometries. How Borges manages to combine such meglomaniacal scale with such subtlely is beyond me. 
 All the rest: less constantly perfect, but still frequently wonderful. Probably my favorite collection of stories, ever.