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This is a state-of-the-art introduction to the work of Franz Reidemeister, Meng Taubes, Turaev, and the author on the concept of torsion and its generalizations. Torsion is the oldest topological (but not with respect to homotopy) invariant that in its almost eight decades of existence has been at the center of many important and surprising discoveries. During the past decade, in the work of Vladimir Turaev, new points of view have emerged, which turned out to be the ""right ones"" as far as gauge theory is concerned. The book features mostly the new aspects of this venerable concept.

Three-manifolds (Topology) --- Reidemeister torsion. --- De Rahm torsion --- Franz torsion --- Reidemeister-Franz torsion --- Torsion, De Rahm --- Torsion, Franz --- Torsion, Reidemeister --- Piecewise linear topology --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds

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Differential topology --- Reidemeister torsion. --- Differentiable mappings. --- Diffeomorphisms. --- Reidemeister, Torsion de. --- Applications différentiables. --- Difféomorphismes. --- Diffeomorphisms --- Differentiable mappings --- Reidemeister torsion --- De Rahm torsion --- Franz torsion --- Reidemeister-Franz torsion --- Torsion, De Rahm --- Torsion, Franz --- Torsion, Reidemeister --- Piecewise linear topology --- Differentiable maps --- Mappings, Differentiable --- Mappings (Mathematics)