Thomas Baldwin's introduction to contemporary philosophy in English is simply outstanding. Baldwin writes very clearly, a great virtue when writing about philosophy and ought not to be unappreciated. Philosophy itself is hard enough and there's no need to add to the confusion by writing badly about it. But in my oppinion Baldwin does a superb job of introducing the main themes and currents of Anglo-American philosophy in the latter half of the 20th century, as well as setting the scene in the first chapter, in a way that everyone can understand and is completely free of all philosophical jargon.
If you want to acquaint yourself with 20th century philosophy, I recommend you start by reading this book. It will get you far and help you put things into perspective. There are also helpful suggestions for further reading in the book. But I also recommend this book to those who are already familiar with 20th century philosophy. You might gain a better perspective of what you're already familiar with, and, again, this book is just fun to read.