Everyone here who knows who Medb is put up your hand. What, not so many?
First off, her name is prounced (more or less) Maeve. She is one of the central characters in the Irish Mythological cycle refered to as the Ulster Cycle and the instigator of the greatest of the Irish epics, the Tain Bo Cuailgne (the Cattle Raid of the Cooley) and should be the great feminist figure from western mythology.
Helen of Troy instigates the Trojan War by essentially running off with a pretty boy and spends the rest of the epic hiding behind the walls of Troy while the heroes fight it out. Except for a moment of giving in she is essentially acted upon rather than an actor. Medb could not be much more different.
The Cattle Raid starts with Medb, the Queen of Connacht, and her current husband (she has worked through a few earlier ones who were unable to abide by her conditions of marriage (more on that below)) having pillow talk over which one of them is the top dog. When they ascertain that he has a better herd of cattle, she will not stand for it an persuades him that he should join her in raiding Ulster to obtain the Dun Cow -- a mighty cow who will push her herd over the top and make sure the right balance of power in the household is restored.
In the adventures that follow Medb is a fully formed character full of strengths and flaws. She is clever, tempermental and ruthless and all times determined to be the commander of her own fate. She is also clear about herself and her expectations about those around ... for example she makes it clear to each of her husbands that they must be free of fear, meanness or jealousy (largely as she has no intention of sticking with one man in any event).
The Irish stories sadly have not had the benefitted from the polishing that the Greek and Roman stories have had. While the characters are far more interesting and the stories are much more humane(all powerful and arbitrary gods play a lesser role; the strengths and foibles of individuals are far more important) they are jerkier and repetitive. Clearly they were more of a grab bag of stories that could be pulled out for the occasion when someone called for a tall tale. All that being said, they are worth the read.