Involutions on Manifolds

0 Notation, Conventions, Preliminaries.- I The Browder-Livesay Invariants.- I.1 Involutions of Spheres.- I.2 Involutions of Simply Connected Manifolds.- II Realization of the Browder-Livesay Invariants.- II.1 The Realization Theorem.- II.2 Constructions with Involutions.- II.3 Proof of Theorem II.1-D.- II.4 Proof of Theorem II.1-A.- II.5 Homology 3-Spheres.- II.6 Manifolds with the Same Regular Homotopy Type as Line Bundles over Projective Spaces.- II.7 Invariant Codimension 2 Spheres.- III Relations with Non-simply-connected Surgery Obstructions.- III.1 Normal Invariants.- III.2 Non-simply-connected Surgery Obstructions.- III.3 Relations with the Browder-Livesay Invariants.- IV Combinatorial Classification of Involutions.- IV.1 Some Maps and Exact Sequences.- IV.2 Computation of [Pn, G/PL].- IV.3 The Classification Theorem.- IV.4 Another Relation with Non-simply-connected Surgery Obstructions.- IV.5 On the Topological Classification of Involutions.- V Smooth Involutions.- V.1 General Remarks on Smooth Involutions of Spheres.- V.2 Normal Invariants and Browder-Livesay Invariants.- V.3 Differentiable Structure of Spheres and Other Double Coverings.- V.4 Proof of Theorem II.1-B, Smooth Case.- V.5 Involutions and the Generalized Kervaire Invariant.- V.6 Smooth Involutions of Spheres of Low Dimension.- V.7 Action of ?n(??) (After Browder).- V.8 How to Prove ? = ?.- VI Codimension 2 Invariant Spheres.- VI.1 Invariant vs. Characteristic Spheres.- VI.2 Applications.- VI.3 Knotted and Unknotted Codimension 2 Invariant Spheres.- VI.4 Cobordism Classes of Invariant Knots.- Some Unsolved Problems.- References.- List of Symbols.