This is a book that I both liked and disliked. The version I read had the 21st chapter that Burgess mentions in the Introduction was left out in the American version, and while I can understand why that was done (to leave an overall good but darker tone to the entire book), it's almost a relief to read the complete version which shows Alex attempting to redeem his past wrongs and grow up.
However, to get to that point, you must first read through the immensely horrifying and disturbing account of his tale at 15 years old (when that was revealed, I was like, 15?? He's 15?? Holy crap), which details his pleasure in beating up helpless individuals, robbery, breaking and entering and rape. The entire beginning is a one step forward, 10 steps back view of Alex, because for every seemingly admirable quality of his (he's smart, he's witty, he's cultured), are his vastly larger number of disturbing traits that make you want to close the book and run away in horror. This is a book that I'm glad to say I have read, though may not do so again.
I have to add a note on the language used in this book, because it is one of the major highlights while reading. As said by others, it might put you off at first due to the confusion of not knowing words, but Burgess does write in a way that becomes understandable after a short while, and not too soon becomes pretty fun to read. In all honesty, it was one of the main reasons why I kept at this book even through the uncomfortable parts - for example, Alex's description of listening to Beethoven in his room is really beautiful (well, until he begins imagining the ultra violence to go along with it). Check out this site for a very useful Nadsat glossary: http://www.visual-memory.co.uk/amk/doc/nadsat.html