I. Poincaré Duality.- § 1. Slant Operations, Cup and Cap Products.- § 2. Poincaré Duality.- §3. Poincaré Pairs and Triads; Sums of Poincaré Pairs and Maps.- §4. The Spivak Normal Fibre Space.- II. The Main Results of Surgery.- §1. The Main Technical Results.- § 2. Transversality and Normal Cobordism.- § 3. Homotopy Types of Smooth Manifolds and Classification.- § 4. Reinterpretation Using the Spivak Normal Fibre Space.- III. The Invariant ?.- § 1. Quadratic Forms over ? and ?2.- §2. The Invariant I(f), (index).- § 3. Normal Maps, Wu Classes, and the Definition of ? for m = 4l.- § 4. The Invariant c(f, b) (Kervaire invariant).- § 5. Product Formulas.- IV. Surgery and the Fundamental Theorem.- § 1. Elementary Surgery and the Group SO(n).- §2. The Fundamental Theorem: Preliminaries.- §3. Proof of the Fundamental Theorem for m odd.- § 4. Proof of the Fundamental Theorem for m even.- V. Plumbing.- § 1. Intersection.- §2. Plumbing Disk Bundles.