This book is primarily directed to graduate students interested in the field and to algebraic topologists who wish to learn something about BP. Beginning with the geometric background of complex bordism, the author goes on to a discussion of formal groups and an introduction to BP-homology. He then presents his view of the major developments in the field in the last decade (the calculation of the homology of Eilenberg-MacLane spaces in this section may be useful in teaching advanced algebraic topology courses). The book concludes with a section on unstable operations with comments on where applications may come from in the future.