This is by far and away my favourite Shakespeare play. It is a very dark and brooding play that is not only incredibly violent, but also ends very badly for most of the main characters. King Lear is one of Shakespeare's great tragedies (along with the Scottish Play and Hamlet) though I find that Hamlet is a lot tighter and the plots are a lot more intertwined than King Lear.
What I mean by this is that there are, I'll say two, plots running side by side and then merge at the end of the play. It is noticeable that both of these plots deal with the same theme, and that is of love. This first plot involves King Lear and the second involves Edgar, his bastard half-brother Edmund, and their father the duke of Gloucester. Lear believes that he has become too old to be a king and decides to divide his kingdom between his daughters, and the biggest portion will go to the one who loves him the most. Two of the daughters put on a song and dance about how much they love him, while the third, who truly loves him, can only be honest. Lear is angered at what he considers a pathetic response, and banishes her from the Kingdom, and divides it between his remaining two daughters. Lord Kent rebukes Lear for this, and Lear banishes him as well.
The Edgar/Edmund plot involves the villain Edmund, who is bitter at being a bastard and schemes to destroy his legitimate brother and take his place. He deceives his father, and Edgar flees to the moors where he disguises himself as Mad Tom, and then brands his father as a traitor (he is aware that the King of France is landing an army in England to restore Lear's third daughter, Cordielia, to the throne, particularly since her sisters have stripped Lear of his kingdom), and then strips him of his dignity by blinding him, and then banishes him to the moors.
As mentioned, the theme of this play is about love. King Lear simply wants to be loved, but does not understand that love is defined by actions not words. This is very clear with Lord Kent who, despite being banished, disguises himself and returns to serve Lear, and despite Lear being stripped of his authority, still recognises him as the true King of England. It is interesting to note that at the close of the play, once Lear has died and Kent is offered the crown, he refuses it, and instead hands it to Edgar, who has been vindicated (and was also the one to defeat Edmund in an epic sword fight). We see a similar theme with Edgar and Gloucester who he finds wondering the moors as a blind man, and assists him to return to his glory (before he dies).
While there is a lot more to this play, another interesting aspect is the division of the kingdom. It is quite anachronistic for the period in which the play was written (or when it was set, in a mythological pre-Roman era – the sources for the play would be Monmouth's Kings of Britain), however during the era of Charlegmaine, this was something that would happen. One's kingdom, and property, were not handed down to the first born, but divided between the male heirs to the throne. This is probably the main reason why Charlegmaine's empire did not last much beyond his lifetime.
I have written a much more detailed analysis, for those who are interested, on my Blog (though this was after watching the Ian McKellan version of the play).