Apollodorus dates from the second century AD, so I've used a picture of a Roman copy of Myron's Discobolus as the picture for this book.
The Library covers much the same material as the Hesiodic Catalogue of Women, but is more complete textually in that about 2½ books out of 3 survive. It's organized by family, but unlike the Hesiodic poem traces descent through the male line rather than the female.
If you've ever tried to read the Bible all the way through, and bogged down at 1 Chronicles, which opens with about 8 chapters of begots, you'll have problems with parts of Apollodoros. Much of the book consists of long lists of parents and children. This is particularly bad when he deals with Heracles and his night of fun during which he supposedly impregnated fifty different women. This feat would earn him a good living in the sleazier areas of LA today. In any case there are long sections that while they may be of interest to the genealogist or the scholar can be lightly skimmed by the general reader.
We get a detailed summary of many of the myths of the ancient world, and get alternate versions of some. We're all familiar with Botticelli's picture of Venus. The drops on the water are the foam generated when the genitals of Cronus were tossed upon the sea. This version was used by both Botticelli and Hesiod. Apollodoros, however, makes her the daughter of Zeus and Dione. This is one variant myth that he gives. There are others, less memorable, but I'll leave it to others to enumerate them.
Apollodoros is not a gifted storyteller, and his renditions of the myths are as dry as some of the entries in Chronicles. For good storytelling you have to go to Apollonius Rhodius and the Argonautica, for a late Greek epic, or Ovid and the Metamorphosis for a Roman mythological epic.
Next up a volume of sf/fantasy short stories A Cosmic Christmas.