This textbook provides a concise introduction to the key concepts and tools of modern statistical mechanics. It also covers advanced topics such as non-relativistic quantum field theory and numerical methods. After introducing classical analytical techniques, such as cluster expansion and Landau theory, the authors present important numerical methods with applications to magnetic systems, Lennard-Jones fluids and biophysics. Quantum statistical mechanics is discussed in detail and applied to Bose-Einstein condensation and topics in astrophysics and cosmology. In order to describe emergent phenomena in interacting quantum systems, canonical non-relativistic quantum field theory is introduced and then reformulated in terms of Feynman integrals. Combining the authors' many years' experience of teaching courses in this area, this textbook is ideal for advanced undergraduate and graduate students in physics, chemistry and mathematics.

This 2006 textbook provides a concise introduction to the key concepts and tools of statistical mechanics. It also covers advanced topics such as non-relativistic quantum field theory and numerical methods. After introducing classical analytical techniques, such as cluster expansion and Landau theory, the authors present important numerical methods with applications to magnetic systems, Lennard-Jones fluids and biophysics. Quantum statistical mechanics is discussed in detail and applied to Bose-Einstein condensation and topics in astrophysics and cosmology. In order to describe emergent phenomena in interacting quantum systems, canonical non-relativistic quantum field theory is introduced and then reformulated in terms of Feynman integrals. Combining the authors' many years' experience of teaching courses in this area, this textbook is ideal for advanced undergraduate and graduate students in physics, chemistry and mathematics.

This book gives a modern presentation of modular operands and their role in string field theory. The authors aim to outline the arguments from the perspective of homotopy algebras and their operadic origin. Part I reviews string field theory from the point of view of homotopy algebras, including A-infinity algebras, loop homotopy (quantum L-infinity) and IBL-infinity algebras governing its structure. Within this framework, the covariant construction of a string field theory naturally emerges as composition of two morphisms of particular odd modular operads. This part is intended primarily for researchers and graduate students who are interested in applications of higher algebraic structures to strings and quantum field theory. Part II contains a comprehensive treatment of the mathematical background on operads and homotopy algebras in a broader context, which should appeal also to mathematicians who are not familiar with string theory.