The second Barcelona Conference on Algebraic Topology was held April 2-8 1986 at the Institut d'Estudis Catalans, Barcelona. The organizing commitee was formed by J. Aguade, M. Castellet, J. Hubbuck, I. James and R. Kane. Titles of the talks delivered at the conference as well as a list of participants are given below. These Proceedings contain transcripts of some of the conference talks as well as related papers. All papers were refereed.Alex Zabrodsky was one of the invited speakers at the conference. It was one of the last conferences he attended. For he died in an automobile accident in New York State in November 1986. A true memorial volume dedicated to Alex will appear in the Israel Journal of Mathematics (of which he was an editor). However we felt it would be inexcusable if these Proceedings did not also record the great sorrow felt by Alex's colleagues at his death. We miss him greatly. We have dedicated the Proceedings to his memory.

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