I Algebraic Theory of Torsions -- 1 Torsion of chain complexes -- 2 Computation of the torsion -- 3 Generalizations and functoriality of the torsion -- 4 Homological computation of the torsion -- II Topological Theory of Torsions -- 5 Basics of algebraic topology -- 6 The Reidemeisterโ{128}{148}Franz torsion -- 7 The Whitehead torsion -- 8 Simple homotopy equivalences -- 9 Reidemeister torsions and homotopy equivalences -- 10 The torsion of lens spaces -- 11 Milnorโ{128}{153}s torsion and Alexanderโ{128}{153}s function -- 12 Group rings of finitely generated abelian groups -- 13 The maximal abelian torsion -- 14 Torsions of manifolds -- 15 Links -- 16 The Fox Differential Calculus -- 17 Computing ?(M3) from the Alexander polynomial of links -- III Refined Torsions -- 18 The sign-refined torsion -- 19 The Conway link function -- 20 Euler structures -- 21 Torsion versus Seibergโ{128}{148}Witten invariants -- References