Contents -- S. P. Novikov's Preface -- 1 J. Milnor. On manifolds homeomorphic to the 7-sphere -- 1. The invariant λ(M7) -- 2. A partial characterization of the n-sphere -- 3. Examples of 7-manifolds -- 4. Miscellaneous results -- References -- 2 M. Kervaire and J. Milnor. Groups of homotopy spheres. I -- 1. Introduction -- 2. Construction of the group Θn -- 3. Homotopy spheres are s-parallelizable -- 4. Which homotopy spheres bound parallelizable manifolds? -- 5. Spherical modifications -- 6. Framed sphericalmodifications -- 7. The groups bP2k -- 8. A cohomology operation -- References -- 3 S. P. Novikov. Homotopically equivalent smooth manifolds -- Introduction -- Chapter I. The fundamental construction -- 1. Morse's surgery -- 2. Relative π-manifolds -- 3. The general construction -- 4. Realization of classes -- 5. The manifolds in one class -- 6. Onemanifold in different classes -- Chapter II. Processing the results -- 7. The Thom space of a normal bundle. Its homotopy structure -- 8. Obstructions to a di.eomorphism of manifolds having the same homotopy type and a stable normal bundle -- 9. Variation of a smooth structure keeping triangulation preserved -- 10. Varying smooth structure and keeping the triangulation preserved.Morse surgery -- Chapter III. Corollaries and applications -- 11. Smooth structures on Cartesian product of spheres -- 12. Low-dimensional manifolds. Cases n = 4, 5, 6, 7 -- 13. Connected sum of a manifold with Milnor's sphere -- 14. Normal bundles of smooth manifolds -- Appendix 1. Homotopy type and Pontrjagin classes -- Appendix 2. Combinatorial equivalence and Milnor's microbundle theory -- Appendix 3. On groups -- Appendix 4. Embedding of homotopy spheres into Euclidean space and the suspension stable homomorphism -- References.

4 S. P. Novikov. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds -- Introduction -- 1. Signature of a cycle and its properties -- 2. The basic lemma -- 3. Theorems on homotopy invariance. Generalized signature theorem -- 4. The topological invariance theorem -- 5. Consequences of the topological invariance theorem -- Appendix (V. A. Rokhlin). Diffeomorphisms of the manifold S2 × S3 -- References -- 5 S. P. Novikov. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots) -- Introduction -- 1. Formulation of results -- 2. The proof scheme of main theorems -- 3. A geometrical lemma -- 4. An analog of the Hurewicz theorem -- 5. The functor P = Homc and its application to the study of homology properties of degree one maps -- 6. Stably freeness of kernel modules under the assumptions of Theorem 3 -- 7. The homology effect of a Morse surgery -- 8. Proof of Theorem 3 -- 9. Proof of Theorem 6 -- 10. One generalization of Theorem 5 -- Appendix 1. On the signature formula -- Appendix 2. Unsolved questions concerning characteristic class theory -- Appendix 3. Algebraic remarks about the functor P = Homc -- References -- 6 R. Kirby. Stable homeomorphisms and the annulus conjecture -- References.