The School on High-Dimensional Manifold Topology took place at the Abdus Salam ICTP, Trieste from 21 May 2001 to 8 June 2001 under the direction of F.T. Farrell (State University of New York at Binghamton) and W. Lück (Westfälische Wilhelms-Universität Münster). The local organizer was Lothar Göttsche (ICTP). The focus of the school was on the classification of manifolds and related aspects of K-theory, geometry, and operator theory. The topics covered included: surgery theory, algebraic K- and L-theory, controlled topology, homology manifolds, exotic aspherical manifolds, homeomorphism and diffeomorphism groups, and scalar curvature. Several conjectures were discussed including those due to: Borel, Novikov, Gromov-Lawson-Rosenberg, Baum-Connes, and Farrell-Jones. This two-part lecture notes volume contains the notes of most of the lecture courses. (ISBN 92-95003-13-6)