Every nationality has its own myths and legends that are part of its heritage, tradition and history. Some say they are also part of a person's psyche, or to put it in more modern vocabulary, the unconscious. If you're not interested in all that, you can still read about mythology for entertainment and to enrich your knowledge and understanding of cultures. Or you can learn about mythology just to brag to your friends about the horrendous mistakes the Hollywood industry makes for the sake of "modernization" when they loosely make a movie about a hero or heroine.
Oddly enough, there are some mythological phenomena that seem to be shared by various and sundry cultures and nations, a fact that has always fascinated ethnologists and anthropologists. For example, the flood... or the explanation for the sunny days towards the end of January. These events may occur with different heroes acting for different reasons, on different impulses, and with the help (or not) of their respective gods; but there is always an underlying theme or chain of events that is common. This is surprising and also very encouraging: we are all the same after all!
Here is a small collection of sources where you can learn about mythology.
(1) Lemprière's Bibliotheca Classica, compiled in 1788 by John Lemprière. A very accurae and useful "Classical Dictionary containing a full Account of all the Proper Names mentioned in Ancient Authors" (its full title).
(2) The Golden Bough, by James George Frazer. Written in 1890, but, in our opinion, still the first book to read, if you want to learn about the mythology of different cultures and their common elements. Untained by modern bladerdash.
(3) The Hero with a Thousand Faces, by Joseph Campbell. Written in 1949. Very good comparative mythology.
(4) The Greek Myths, written in 1955 by the poet and scholar Robert Graves. Excellent interpreations, which, although rejected by academic scholars, provide a deep inside into the matriarchal structure of society in pre-historic Greece.
(5) Mythology: Timeless Tales of Gods and Heroes by Edith Hamilton (1942). Very comprehensive introduction to Greek mythology.
(6) Finally, a list of sites which are about Greek mythology. Some good... some very good:
This should be enough. Whatever you do,