This manuscript was a pretty good find, or at least the sections that we did find to complete the manuscript that was handed down to us, because it gives us all of those Greek stories that we know and love, from this:
and finished of with this:
but unfortunately it does not contain this:
The book is actually only a brief overview of each of the legends and is divided into a number of sections which outline various Greek families, or tribes, so the book is not strictly chronological. What the library does is that it gives us a brief rundown of the legends that make up the mythology of the Ancient Greeks as it existed at the time of Apollodorus. In fact, it is the earliest complete outline of Greek mythology that we possess (though it is not necessarily complete because sections of the manuscript were lost, however a fortuitous discovery in the Vatican library allowed us to reconstruct most of it). This is not the only complete source that we have because we also have Ovid's Metamorphoses, however the difference between Apollodorus and Ovid is that Ovid writes from Roman point of view, so is a lot more sympathetic towards the Trojans. Ovid is also wrote the Metamorphoses as an epic poem (which excludes the genealogies) as opposed to an outline, which is how Apollodorus wrote the library.
The library is full of genealogies, which outlines the parentage of many of the Greek heroes and demigods, and it also divides them into a number of tribes, being the Deucalionids (from which comes Jason and the Argonauts), the Argives (from which comes Heracles), the Anegorid, the Inachids, the Asopids, and the Pelopids. Each of these tribes (the members all have a common ancestry) come from different parts of Greece, which suggests that the myths that come out of the tribes originated from this part of Greece (and Ancient Greece was not a unified country, but rather a loose collection of city states that shared a common language and culture, and even then the various city states would war against each over because of an accent or a disagreement that originated in mythology – which is what still seems to be happening today, except on a much larger scale).
There is an interesting distinction between history and myth that comes out in Herodotus. The common understanding of myth is that it is a story that suggests an origin, and it does not necessarily mean that the story is not true. Herodotus takes a different position in that history is written down, where as myth is passed down by word of mouth. As such the writings that create history are written down while still within living memory, while myth comes about after generations of passing the story down, which suggests that the story may have been true, however it has become corrupted as it has been passed down from generation to generation.
Take for instance the story of Achilles. In the Illiad there is no mention of his invulnerability due to being dipped into a river. This is not even the story that occurs in the library as the story that occurs here is that Achilles' mother would bury him in fire at night and rub him with ambrosia during the day. The story about Achilles being dipped into the River Styx did not appear until the 1st Century AD, in a book (now lost) known as the Achilleid. As you can see, as time passes, the stories become more and more corrupted (and that occurs even with an original story having been written down).
This book gives me a lot of opportunities to speculate on the truth behind many of these tales, though we also have earlier sources which we can also refer to, being the tragic plays and the epic poems, however these sources tend to focus mainly on the Trojan War, with the other stories only touched upon (and I believe that the Library is the earliest source for the story of Perseus, though he does receive a mention in Herodotus, but there we are only told that he married Andromeda and that he because the ancestor of the Persians).