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Heroes, Gods & Trojan Horses: Classic Mythology Revisited
Greek Gods and HeroesGreek Gods and Heroes by Robert Graves
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IMHO the best secondary source on classic mythology; by Roman emperor Claudius the Stutterer's (fictional) biographer ("I, Claudius;" "Claudius the God"): Well-written, informative and comprehensive.
Theogony and Works and Days (Oxford World's Classics)Theogony and Works and Days (Oxford World's Classics) by Hesiod
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One of the oldest primary sources on the Olympian gods, their ancestors and progeny and the creation of the world according to Greek mythology (partly differing from Homer, though).
The Homeric Hymns (Oxford World's Classics)The Homeric Hymns (Oxford World's Classics)
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In fact the work of several poets, these in addition to the Iliad and the Odyssey constitute the core of (originally orally transmitted) Greek mythology.
The Iliad: the OdysseyThe Iliad: the Odyssey by Homer
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The 2 best-known works associated with Homer in an acclaimed new translation: the 10-year Trojan War & the Trojan horse creator's 20-year-journey home. (Both originally transmitted only orally, too.)
The Aeneid (Everyman's Library classics)The Aeneid (Everyman's Library classics) by Virgil
Buy new: £7.69 / Used from: £6.94
Ancient Rome's companion piece to the above; the wanderings of the forefather of Romulus and Remus, Rome's mythical founders. Composed by Virgil and commissioned by emperor Augustus himself.
The Early History of Rome: Bks. 1-5 (Penguin Classics)The Early History of Rome: Bks. 1-5 (Penguin Classics) by Livy
Buy new: £6.68 / Used from: £6.70
Rome's mythical foundation, lore and early history, artfully told in the classic text authored by Virgil's contemporary, Augustan historian Titus Livy.
The Metamorphoses: a New Verse Translation (Penguin Classics)The Metamorphoses: a New Verse Translation (Penguin Classics) by Ovid
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The foremost Roman collection of classic mythology; both Greek and Roman. The one must-read besides the Iliad, the Odyssey and the Aeneid, even if you're not looking at any other primary sources.
The Voyage of ArgoThe Voyage of Argo by Apollonius of Rhodes
Buy new: £6.19 / Used from: £0.29
The most comprehensive primary version of the tale of Jason and the Golden Fleece (Jason's ill-fated wife Medea in particular later also became the subject of several plays, though; see below).
The Voyage of the "Argo": The Argonautica of Gaius Valerius FlaccusThe Voyage of the "Argo": The Argonautica of Gaius Valerius Flaccus
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A few centuries later, Apollonius's humanly flawed hero becomes the stuff of one of literary history's first great (albeit sadly uncompleted) tales of adventure and bravery.
The Complete Greek Tragedies: Aeschylus v.1: Aeschylus Vol 1The Complete Greek Tragedies: Aeschylus v.1: Aeschylus Vol 1 by Grene
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By the father of the Greek tragedy: Sacrifice, murder and revenge at the beginning and the end of the Trojan War in king Agamemnon's house, but new civilization arises under Athena's guidance at last.
The Complete Greek Tragedies: Aeschylus, Pt.2 v. 2The Complete Greek Tragedies: Aeschylus, Pt.2 v. 2 by Grene
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Aeschylus on Prometheus (fire for humanity, torture ever after); Danaus's 50 daughters in Argos ("The Suppliants"); patricide & incest ("7 Against Thebes"); and the battle of Salamis ("The Persians").
The Complete Greek Tragedies: Sophocles, Pt.1 v. 8The Complete Greek Tragedies: Sophocles, Pt.1 v. 8 by Grene
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Sophocles's famous cycle about Oedipus, king of Thebes, who (unknowingly) kills his father and marries his own mother; and Antigone, who defends her divine right even if she has to die for it.
The Complete Greek Tragedies: Sophocles Vol IIThe Complete Greek Tragedies: Sophocles Vol II by Grene
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Sophocles's non-Thebes plays (Troy in 3 of 4): Embittered warrior Ajax; woeful Electra (Orestes's sister/Agamemnon's daughter); wounded & betrayed Philoctetes; plus Heracles's tragic wife Deianeira.
The Complete Greek Tragedies: Euripides Vol 1 (Euripides)The Complete Greek Tragedies: Euripides Vol 1 (Euripides)
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Euripides's take on Alcestis's self-sacrifice for her husband's life; Medea's fate after marrying Jason; Heracles's children in Athens (Heracleidae); and Hippolytus, Theseus, Phaedra and Aphrodite.
The Complete Greek Tragedies: Euripides Vol 2: Euripides Vol 4The Complete Greek Tragedies: Euripides Vol 2: Euripides Vol 4 by Grene
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Euripides on Odysseys and Polyphemos the Cyclops; Heracles and divine malice; Iphigenia after being sacrificed by Agamemnon; and an alternative history of Helen (Egypt instead of Troy!).
The Complete Greek Tragedies: Euripides Vol 3: Euripides Vol 5The Complete Greek Tragedies: Euripides Vol 3: Euripides Vol 5 by Grene
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The Trojan War seen from a female perspective: Hecuba, Andromache, other Trojan Women and life's unpredictability; plus Ion, Apollo's unjustly unacknowledged son.
The Complete Greek Tragedies: Euripides Vol 4: Euripides Vol 6The Complete Greek Tragedies: Euripides Vol 4: Euripides Vol 6 by Grene
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Rhesus, Troy's failed savior (is this truly by Euripides?); war and the rule of law (Suppliant Women); Agamemnon's sacrifice before going to Troy (Iphigenia) and Orestes's post-matricide lot.
The Complete Greek Tragedies: Euripides Vol 5The Complete Greek Tragedies: Euripides Vol 5
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Euripides on Electra (different from Sophocles & Aeschylus!); the battle for Thebes between Oedipus's sons (The Phoenician Women); and king Pentheus' refusal to worship Dionysos (The Bacchae).
Aesop's Fables (Penguin Popular Classics)Aesop's Fables (Penguin Popular Classics) by Aesop
Buy new: £2.16 / Used from: £0.01
No mythology, but a popular favorite practically ever since the time of their first collection in writing 2 millenia ago and probably as influential as any play by Aeschylus, Sophocles, Euripides etc.
The Gods of the GreeksThe Gods of the Greeks by C. Kerényi
Buy new: £7.11 / Used from: £1.46
Background information on the mythological deities' cultural, spiritual and psychological importance in the context of ancient Greek society and of the humanistic tradition as a whole.
The Heroes of the GreeksThe Heroes of the Greeks by C. Kerényi
Buy new: £8.96 / Used from: £1.17
Kerenyi's companion volume to "Gods of the Greeks" ...
Athene - Virgin and Mother in Greek Religion: Study of Pallas Athene (Dunquin Series: No. 9)Athene - Virgin and Mother in Greek Religion: Study of Pallas Athene (Dunquin Series: No. 9) by Carl Kerenyi
Buy new: £14.99 / Used from: £6.72
...and his look at Zeus's daughter/advisor, the patroness of wisdom, warfare & the city of Athens (also part 2 of my screen name; part 1 is a Titan, Greek mythology's equivalent of Iustitia: justice).
Remus: A Roman MythRemus: A Roman Myth by T.P. Wiseman
Buy new: £19.94 / Used from: £11.25
A modern examination of Roman mythology, as seen particularly in the context of the city's foundation.
Bullfinch's Mythology (Modern Library)Bullfinch's Mythology (Modern Library) by Thomas Bulfinch
Buy new: £9.39 / Used from: £4.80
The standard before Graves's book (see above #1); more detailed - originally published in 3 parts & a true brick when compiled in 1 volume - but primarily for those seriously interested in this area.
Mythology (Back Bay books)Mythology (Back Bay books) by Edith Hamilton
Buy new: £7.32 / Used from: £2.46
If all you want is a brief introduction, though, Edith Hamilton's "Mythology" (or her even shorter "Timeless Tales of Gods and Heroes") will probably do just fine - it even covers Norse myths as well.