Proof Theory The First Step into Impredicativity

From the reviews:

"Proof Theory takes various axiom systems … that treat induction in different ways and analyzes them from the ordinal viewpoint to gauge their relative strengths. … This new version includes several developments in the field that have occurred over the twenty years since the original. Although the current book, appearing in the Universitext series, claims to be ‘pitched at undergraduate/graduate level,’ an undergraduate course out of Proof theory would be ambitious indeed." (Leon Harkleroad, The Mathematical Association of America, March, 2009)

"The book is addressed primarily to students of mathematical logic interested in the basics of proof theory, and it can be used both for introductory and advanced courses in proof theory. … this book may be recommended to a larger circle of readers interested in proof theory." (Branislav Boricic, Zentrablatt MATH, Vol. 1153, 2009)