Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing res

The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains a

This should be a useful reference for anybody with an interest in quantum theory.

One of the aims of this book is to explain in a basic manner the seemingly difficult issues of mathematical structure using some specific examples as a guide. I