"Advances in Proof Theory" is a scholarly book that addresses the latest developments in proof theory, constructivity, and computation. It brings together original contributions from leading specialists in the field and highlights current trends and results. A particular focus is placed on topics such as ordinal analysis, reductive proof theory, explicit mathematics, and type-theoretic formalisms. The book is a tribute to Professor Gerhard Jäger, who significantly contributed to the promotion of logic in Switzerland. The contributions stem from a symposium held in Bern in 2013 and reflect the significant role of proof theory in mathematical and philosophical logic. This discipline, initiated by David Hilbert in the 1920s, has evolved into an essential component of the foundations of mathematics and is particularly relevant to questions in computer science.