I had to read both Medea and Hecabe as part of background reading to some courses on Greek Mythology and Shakespeare during my degree. 'Medea' came as a surprise offshoot mythological tale to the aftermath of Jason (from the Argonauts) and Medea's union towards the end of Apollonius' 'Jason and the Golden Fleece'. The romantic, flowery love affair we see at the end of the tale turns out a sordid, tragic affair some 10 years later in Euripides' version after they're married with children. Betrayal, jealousy, self-doubt and eventual infanticide and suicide makes it one of the most horrific tales of human tragedy.
What makes Euripides so brilliant is his very human portrayal of the characters. You feel for them, you empathize with them, and you can anticipate their every emotional decision and thoughts of self-reflection. 'Hecabe', similarly deals with the immediate aftermath of the Trojan War and the death of the Trojans at the hands of the Achaens. Hecuba is the wife of Priam and mother of all the major Trojan warriors: Hector, Paris, Aeneus. She is grieving for the death of her husband and all her sons, except one and her daughter. She witness their deaths too, and her agony at the merciless hands of the Greeks (including Odysseus, whom we see here as very severe and inhumane, in contrast to his central heroic role in The Odyssey) make her suffering tragic beyond words. It was recently played in the West End by two productions in 2005.
I would suggest this book simply for the mastery of Euripides and his psychological dimension in human tragedy. Just because it is 'ancient' literature and a translation of the old Greek, does not in any way detract it from being so relevant and significant to the modern world. Raw human emotions, and you don't get that in today's literature much.