The stationary tower is an important method in modern set theory invented by Hugh Woodin in the 1980s. It is a means of constructing generic elementary embeddings and can be applied to produce a variety of useful forcing effects. Hugh Woodin is a leading figure in modern set theory, having made many deep and lasting contributions to the field, in particular to descriptive set theory and large cardinals. This book is the first detailed treatment of his method of the stationary tower that is generally accessible to graduate students in mathematical logic. It should become the standard reference on the stationary tower and its applications to descriptive set theory. The book is suitable for a graduate course that assumes some familiarity with forcing, constructibility, and ultrapowers.