An introduction to tensor product spaces -- Proximinality -- The alternating algorithm -- Central proximity maps -- The diliberto-straus algorithm in C(S ร{151} T) -- The algorithm of von golitschek -- The L 1-version of the diliberto-straus algorithm -- Estimates of projection constants -- Minimal projections -- Appendix on the bochner integral -- Appendix on miscellaneous results in banach spaces