The subject of BP-theory has grown dramatically since the appearance of the first edition 17 years ago. One major development was the proof by Devinatz, Hop- kins and Smith (see Devinatz, Hopkins and Smith [1] and Hopkins and Smith [2]) of nearly all the conjectures made in Ravenel [8]. An account of this work can be found in our book Ravenel [13]. The only conjecture of Ravenel [8] that remains is Telescope Conjecture. An account of our unsuccessful attempt to disprove it is given in Mahowald, Ravenel, and Shick [1].
Another big development is the emergence of elliptic cohomology and the theory of topological modular forms. There is still no comprehensive introduction to this topic. Some good papers to start with are Ando, Hopkins and Strickland [1], Hopkins and Mahowald [1], Landweber, Ravenel and Stong [8], and Rezk [?], which is an account of the still unpublished Hopkins-Miller theorem.
The seventh and final chapter of the book has been completely rewritten and is nearly twice as long as the original. We did this with an eye to carrying out future research in this area.
I am grateful to the many would be readers who urged me to republish this book and to the AMS for its assistance in getting the original manuscript retypeset. Peter Landweber was kind enough to provide me with a copious list of misprints he found in the first edition. Nori Minami and Igor Kriz helped in correcting some errors in § 4.3. Mike Hill and his fellow MIT students provided me with a timely list of typos in the online version of this edition. Hirofumi Nakai was very helpful in motivationg me to make the revisions of Chapter 7.