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Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, supersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.

Topology. --- Geometry. --- Mathematical physics. --- Topologie --- Géométrie --- Physique mathématique --- Physics. --- Global differential geometry. --- Mathematical Methods in Physics. --- Physics beyond the Standard Model. --- Differential Geometry. --- Topology --- Geometry --- Mathematical physics --- Applied Physics --- Physics - General --- Engineering & Applied Sciences --- Physics --- Physical Sciences & Mathematics --- Physical mathematics --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Natural philosophy --- Philosophy, Natural --- Mathematics --- Differential geometry. --- Quantum field theory. --- String theory. --- Quantum Field Theories, String Theory. --- Geometry, Differential --- Differential geometry --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Physical sciences --- Dynamics --- String models. --- Geometry, Differential.