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In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Ge

Quantum theory. --- Geometric quantization. --- Topology. --- Mathematical physics. --- Physical mathematics --- Physics --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Geometry, Quantum --- Quantization, Geometric --- Quantum geometry --- Geometry, Differential --- Quantum theory --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Mathematics