The most common way for people to learn about Greek and Roman mythology today is to read anthologies of tales or modern works that use the mythology as a basis. Anyone wishing a deeper knowledge of mythology, though, will want to return to its original sources and greatest works. And although some myths originate with Roman sources or are modified in interesting ways by the Romans, most of the myths in this tradition that have survived come from the Greeks.
What follows are some of the most significant works of Greek mythology. Not all are the earliest surviving sources of particular Greek mythology stories (though many are), but they are the definitive versions.
Greek Epics
The two most important mythological works of any kind are the Iliad and the Odyssey. These works, both attributed to the blind poet Homer, are therefore an excellent starting point for examining Greek mythology's sources. The Iliad tells a portion of the story of the Trojan War, focusing on Achilles and climaxing with Achilles' killing of the Trojan hero Hector. The Odyssey tells of the long homeward journey of Odysseus after the war, and the various dangers he faces along the way – Cyclopes, sirens, Circe the sorceress, and so forth.
Hesiod is responsible for a different sort of epic poem with his Theogony. This poem tells a variety of stories on the same theme: the origin of the world and the birth of the various gods. Its organized description of the various gods' relations is responsible for giving us a better understanding of how various Greek gods and myths fit together.
A far later epic called Argonautica tells of Jason's quest for the Golden Fleece. It was written by Apollonius of Rhodes, and is significantly shorter than the epics of Homer. Its narrative of Jason's collecting a band of heroes called Argonauts, their dangerous voyage, and the successful acquisition of the Golden Fleece with the help of Medea is the definitive version of the tale.
Greek Tragedy
The three great Greek tragedians all specialized in dramas derived from mythology, and in some cases their dramas are the only surviving sources of particular tales. Aeschylus is best known for his Oresteia trilogy, consisting of three plays (Agamemnon, The Libation Bearers, and Eumenides) detailing the murder of Agamemnon upon his return from Troy, and the cycle of vengeance that followed. Two of his other well-known plays are Prometheus Bound and Seven Against Thebes.
Sophocles' best known tragedies are those dealing with the family of Oedipus. Oedipus Rex (or Oedipus the King) details the tragedy that ensues when Oedipus, the king of Thebes, learns the truth about his father and mother. Oedipus at Colonus deals with the aftermath of the exile of Oedipus. Antigone focuses on his titular daughter and her struggle to bury her rebellious brother's body contrary to the decree of Creon, now king of Thebes.
There are more surviving tragedies by Euripides than either of the above playwrights. His most significant plays include Medea, the Bacchae, and Iphigenia at Aulis. Those plays deal with, respectively, Medea's murder of her children to revenge herself on Jason, the consequences Dionysus visits upon Pentheus when he refuses to worship Dionysus, and Agamemnon's sacrifice of his daughter Iphigenia to gain favorable winds to sail to besiege Troy.
The Odes of Pindar
One final significant source of Greek mythology is the odes of the poet Pindar. His odes generally celebrate athletic accomplishment, but typically include the retelling of a relevant myth in the course of the poem. These myths are sometimes modified from other versions; thus, as with different playwrights addressing the same stories, Pindar provides an alternate perspective for the myths.
All the works mentioned above have been important sources of mythology, first for the Romans, who often drew heavily on them when writing their own literature, and since for numerous other authors who have retold or modified the myths. Going back to any of these originals will reveal the essence of these influential myths.