This volume and its companion present a selection of the mathematical writings of P. R. Halmos. The present volume consists of research publications plus two papers which, although of a more expository nature, were deemed primarily of interest to the specialist ("Ten Problems in Hilbert Space" (1970d), and" Ten Years in Hilbert Space" (1979b)). The remaining expository and all the popular writings are in the second volume. The papers in the present volume are arranged chronologically. As it happens, that arrangement also groups the papers according to subject matter: those published before...