Serreʹs contribution to the development of algebraic topology

We describe in detail Serreʹs application of spectral sequence theory to the study of the relations between the homology of total space, base space and fibre in a Serre fibration; and we apply the results to establish that a 1-connected space X has homology groups (in positive dimension) in a Serre class C if and only if its homotopy groups are in C. We include in this paper some personal reflections on the contact the author had with Serre during the decade of the 1950ʹs when Serreʹs revolutionary work in homotopy theory was completely changing the face of algebraic topology.