This book aims to fill the gap in the available literature on supermanifolds, describing the different approaches to supermanifolds together with various applications to physics, including some which rely on the more mathematical aspects of supermanifold theory.

The first part of the book contains a full introduction to the theory of supermanifolds, comparing and contrasting the different approaches that exist. Topics covered include tensors on supermanifolds, super fibre bundles, super Lie groups and integration theory.

Later chapters emphasise applications, including the superspace approach to supersymmetric theories, super Riemann surfaces and the spinning string, path integration on supermanifolds and BRST quantization.

Contents:

• Super Algebras
• Superspace
• Functions of Anticommuting Variables
• Supermanifolds: The Concrete Approach
• Functions and Vector Fields
• Supermanifolds: The Algebro-Geometric Approach
• The Structure of Supermanifolds
• Super Lie Groups
• Tensors and Forms
• Integration on Supermanifolds
• Geometric Structures on Supermanifolds
• Supermanifolds and Supersymmetric Theories
• Super Riemann Surfaces
• Path Integrals on Supermanifolds
• Supermanifolds and BRST Quantization
• Supermanifolds and Geometry

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