The story of the Trojan horse isn't found in the Iliad, nor is the account of Achilles' death. Some of the main sources we have for Greek mythology, such as the preceding examples, come from the mythographers, i.e. Apollodorus and Hyginus. They fill in many gaps in our knowledge of Greek mythology. They recount the genealogy of the gods and tells of their amorous exploits and offspring. Not all of the tales are fabulous either. Some seem to be grounded in very possible history. Intrigues, wars, murders and many other subjects are recounted. One can conclude that many of the Greek playwrights were originally either inspired by handbooks such as these, or, possibly, from oral tradition. Chances are good when one reads more current mythogoraphical works like those of Robert Graves or Thomas Bulfinch, one will undoubtedly encounter these earlier mythographers as primary sources. What these works lack in poetic flair, they make up for in simply providing details.
As far as Greek mythology is concerned, Hyginus and Apollodorus are essential sources. They are later than Hesiod and Homer undoubtedly, but the traditions they recount are probably much older. The only other notable sources we have for Greek mythology comes from various odes, fragments, lyric poets and the tragedians and the comedians.
I have to say that I was put off by some of the phrasing chosen by the translators here. It is off putting when ancient thought is twisted into modern idiom. I suppose I prefer Romantic and Victorian phrasing and would probably opt for high (for lack of a better word) English than 21st century vernacular English.