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内容説明 A representative survey of developments in relativistic and non-relativistic quantum theory， which are related to the application of symmetries in their most general sense. The corresponding mathematical notions are centred upon groups， algebras and their generalizations， and are applied in interaction with topology， differential geometry， functional analysis and related fields. Special emphasis is on results in the following areas: quantization methods， non-linear evolution equations， foundation of quantum physics， algebraic quantum field theory， gauge and string theories， quantum information， quantum groups， and discrete symmetries.