Set Theory

The author tried to cover everything a set theorist should master plus a representative selection of topics of current interest. That makes for a lot of ground to cover, but Jech did a great job. The writing is very well organized and clear. Every short chapter has many exercises, often with hints. There are extensive sections on applications of forcing. The indexes are really good.There has to be a down side, of course. In order to squeeze so much in, he had to be brief. There is little context provided, especially in Part I: Basic Set Theory. There are rarely any examples and only the main facts are covered. That is all part of an understandable compromise, but I have a serious complaint (my only one) about the references. He gives detailed historical references in each chapter, but no references to further reading. He could have done it with hardly any use of space and it would have been very helpful.Because of the brevity, it is a bit hard to learn from, but it makes a great secondary reference. For example, its explanations are often clearer and more direct than in Kunen and with more detailed proofs. It you are going to have any more exposure to set theory than an introductory course, you will probably want to buy a copy. (BTW, the 2e was just a corrected reprint; 3e is a complete rewrite.)