With one exception, these papers are original and fullyrefereed research articles on various applications ofCategory Theory to Algebraic Topology, Logic and ComputerScience. The exception is an outstanding and lengthy surveypaper by Joyal/Street (80 pp) on a growing subject: it givesan account of classical Tannaka duality in such a way as tobe accessible to the general mathematical reader, and toprovide a key for entry to more recent developments andquantum groups. No expertise in either representation theoryor category theory is assumed. Topics such as the Fouriercotransform, Tannaka duality for homogeneous spaces, braidedtensor categories, Yang-Baxter operators, Knot invariantsand quantum groups are introduced and studies.From the Contents: P.J. Freyd: Algebraically completecategories.- J.M.E. Hyland: First steps in synthetic domaintheory.- G. Janelidze, W. Tholen: How algebraic is thechange-of-base functor?.- A. Joyal, R. Street: Anintroduction to Tannaka duality and quantum groups.- A.Joyal, M. Tierney: Strong stacks andclassifying spaces.- A.Kock: Algebras for the partial map classifier monad.- F.W.Lawvere: Intrinsic co-Heyting boundaries and the Leibnizrule in certain toposes.- S.H. Schanuel: Negative sets haveEuler characteristic and dimension.-