A page of mathematical autobiography.--On certain numerical invariants of algebraic varieties, with application to Abelian varieties.--Intersections and transformations of complexes and manifolds.--Manifolds with a boundary and their transformations.--L'analysis situs et la géométrie algébrique.--Invariance absolue et invariance relative en géométrie algébrique.--Locally connected sets and their applications.--Singular and continuous complexes, chains, and cycles.--Complete families of periodic solutions of differential equations.--On singular chains and cycles.--On generalized manifolds.--Chain-deformations in topology.--Closed point sets on a manifold.--On transformations of closed sets.--On compact spaces.--On separable spaces.--On locally connected and related sets.--On the fixed-point formula.--Bibliography (p. [627]-639)