"The Age of Fable" is a compendium of the myths of ancient Greece and Rome, and also some Celtic, Norse, Egyptian and Eastern myths. First published in 1855, it retained popularity for a long time afterwards. It's divided into short chapters of about 8 pages each, and told in a very readable style. Its most distinctive feature is that at the end of each tale, it includes a couple of paragraphs on the literary allusions it has inspired. 18th and 19th century poets like Byron, Keats, and Pope were steeped in these myths, so they're quoted a lot, along with various others.
Bulfinch's preferred source for the myths is, according to Roger Lancelyn Green's curiously ambivalent introduction, Ovid's "Metamorphosis", though he also uses myths not found in that book. He uses the Roman names rather than the Greek (e.g. "Ulysses", not "Odysseus"), though he includes the Greek in parentheses when first introducing the characters. All the myths are here, from the birth of the gods, through Pandora's box, Phaeton's chariot, the abduction of Proserpine, the siege of Troy, Ulysses, Aeneas, and dozens of others.
Bulfinch's use of language is elegant without being fussy, a slightly elevated language very appropriate for these myths. He tells the stories very well so this is very good and readable introduction to the myths and a good reference tool, though the index to this edition isn't great (Everyman edition 1969- though Amazon might move this review to other editions), only listing the first appearance of each character in the book- then again, the chapter headings usually give the main characters therein.
Looking on this site, it appears that newer editions of this book are titled "Bulfinch's Mythology". Seems like it's the same book, just a name change.