The Eumenides sometimes known as The Furies, is the final play of the Oresteia, a sequence by Aeschylus, originally produced at Athens in 458 BC, when it won that year's dramatic competition. Along with its precursors, Agamemnon and The Libation Bearers, it forms the only trilogy from classical Attic tragedy to survive in full, although an accompanying satyr-play, the Proteus is lost.
The plot opens with the Furies, goddesses of vengeance, in pursuit of Orestes, who has killed his own mother, Clytemnestra, in revenge for her killing of his father Agamemnon. Orestes flees first to the shrine of Apollo at Delphi, and then to Athens, where Athena arranges his trial by the court of Areopagus. The theme of the play is thus revealed as the transition from clan-based vengeance to the justice of the polis.
Free online texts
Gutenberg: The House of Atreus; Being the Agamemnon, the Libation bearers, and the Furies, translated by E.D.A. Morshead. Multiple formats.
Internet Archive: The Plays of Aeschylus, translated by Walter Headlam and C.E.S. Headlam. Multiple formats.
Loebulus. L146 - Aeschylus -- Agamemnon. Libation-Bearers. Eumenides. Fragments. PDF of public domain Loeb edition in Greek and English.
Poetry in Translation: Eumenides, translated by George Theodoridis (2009). Multiple formats.
University of Adelaide (Internet Archive): The Eumenides, translated by E.D.A. Morshead. Multiple formats.
Vancouver Island University: The Eumenides (The Kindly Ones), translated by Ian Johnston. HTML format.
History of Ancient Greece: Early Tragedy and Aeschylus, podcast by Ryan Stitt.
Librivox: The Furies (Morshead Translation), public domain audiobook.
Literature and History: Episode 26 - Ancient Greek Theater. Podcast by Doug Metzger.
Literature and History: Episode 29 - The Mound and the Furies - The Oresteian Trilogy, Part 3: The Eumenides. Podcast.
The Great Conversation: Further reading at Tom's Learning Notes
Aristotle: The Poetics.
A.E. Haigh: The Tragic Drama of the Greeks (1896).
Ancient Greek resources: Learn to read Greek classics in the original.