“The Theory of Electron-Atom Collisions” should find a place not only with the professional quantum theorists but with those physicists who require merely to understand the effects produced by elastic and inelastic collisions, without personally manipulating the mathematics. No longer is it possible for the more classically inclined ionized gas physicist to aver that the quantum theory methods only nibble at the collision problem. Consider the achieve­ments as of 1964: the ability to predict elastic scattering and excitation functions for simple atoms, with pointers in the direction of success for many-electron atoms; the prediction of the existence of virtual and real energy levels, and the scattering effects they produce; the establishment of upper limits with confidence which is far greater than that usually applied to theoretical cross-sections; the prediction of scattering cross-sections for electrons with ions and with excited atoms, collisions which have hardly yet been attempted in experiment. Only in ionizing collisions is the theoretical position rather less satisfactory.