I know that much of Greek mythology was passed on by word of mouth but someone must have been the first to collect this in one source. What was that Compendium and is there a version available in modern English?
According to Wikipedia,
"the only general mythographical handbook to survive from Greek antiquity was the Library of Pseudo-Apollodorus."
Also good to note, the work is incomplete. There are three (known) books fallling under this umbrella. A portion of the third volume has been lost. This site shows the chapters by text ending at Thesus, similar to the Wikipedia posting.
The book is a compilation, taking pieces from ancient Greek epics and plays. This excerpt lists some of the genealogy of the titans:
"[1.1.3] And again he begat children by Earth, to wit, the Titans as they are named: Ocean, Coeus, Hyperion, Crius, Iapetus, and, youngest of all, Cronus; also daughters, the Titanides as they are called: Tethys, Rhea, Themis, Mnemosyne, Phoebe, Dione, Thia."