Title: Bredon homology and equivariant K-homology of SL(3,Z) Author: Ruben Sanchez-Garcia Author's address: Department of Pure Maths, Hicks Building University of Sheffield Sheffield S3 7RH, United Kingdom Included ps or eps files: SouleFundamentalDomainLabelled.eps TruncatedCube.eps AMS classification number: 19L47, 55N91 (Primary); 19K99, 46L80 (Secondary) Other useful information: arXiv:math.KT/0601587 Abstract: We obtain the equivariant K-homology of the classifying space \underline{E}SL(3,Z) from the computation of its Bredon homology with respect to finite subgroups and coefficients in the representation ring. We also obtain the corresponding results for GL(3,Z). Our calculations give therefore the topological side of the Baum-Connes conjecture for these groups.