For (optional) further reading, here is a very short list of personal favorites to help you get started. Almost all of the books have bibliographical appendices with further suggestions.

General

A good general introduction is Bernhard Zimmermann (Thomas Marier, tr.), Greek Tragedy: An Introduction (Johns Hopkins, 1991). Zimmermann in an appendix lists in annotated fashion many of the best works on Aeschylus, Sophocles, and Euripides.

On links between tragedy and earlier Greek poetic traditions, John Herington, Poetry into Drama (California, 1985) is simply splendid.

Ancient theater and stagecraft

Good as an introduction to the stagecraft of ancient theater is Rush Rehm, Greek Tragic Theater (Routledge, 1992). For a quick overview, see the account by John Gould ("Tragedy in Performance") in Cambridge History of Classical Literature, vol. 1, Greek Literature, ed. P. E. Easterling and B. M. W. Knox (Cambridge, 1985) 263-80, with bibliography on pp. 759-761.

Specific interpretations of the plays in light of what we know about theater and performance will be found in Oliver Taplin, Greek Tragedy in Action (California, 1978).

The fundamental scholarly resource for details about context and performance of the plays is A. Pickard-Cambridge, Dramatic Festivals of Athens, 2nd ed. rev. J. Gould and D. M. Lewis (Oxford, 1968).

Aeschylus

Far the best introduction to Aeschylus, and good also as a general introduction to tragedy, is John Herington, Aeschylus (Yale, 1986). Thomas G. Rosenmeyer, The Art of Aeschylus (California, 1982) is not only a good (if dense) book in its own right, but offers good bibliographies on the individual Aeschylean plays.

Sophocles

Most book-length work focuses on the Sophoclean hero. Two of the great books on this subject (if now a bit old fashioned) are B. M. W. Knox, The Heroic Temper: Studies in Sophoclean Tragedy (California, 1964) and R. P. Winnington-Ingram, Sophocles: An Interpretation (Cambridge, 1980). On the subject of the Sophoclean hero more generally, taking into account the many later dramatists who based their work on Sophocles, see G. Steiner, Antigones (Oxford, 1984).

Euripides

Euripides is a more difficult subject, as views on Euripides seem to change continuously, and there are fewer landmark works of enduring use. But a good sampling of recent views on Euripides can be found in P. Burian, Directions in Euripidean Criticism (Durham, 1985). For a more general overview, see the chapter on Euripides in the Cambridge History of Classical Literature, vol. 1, Greek Literature, ed. P. E. Easterling and B. M. W. Knox (Cambridge, 1985), with the bibliographic appendix.