This chapter summarizes the theory of electron collisions with atoms, ions, and molecules. Section 49.1 discusses elastic, inelastic, and ionizing collisions with atoms and atomic ions from close to threshold to high energies where the Born series becomes applicable. Section 49.2 extends the theory to treat electron collisions with molecules. Finally, the theory of electron–atom collisions in intense laser fields is discussed in Sect. 49.3. This chapter will not present detailed comparisons of theoretical predictions with experiment. Such comparisons are given in many books and review articles, such as 1 ; 2 ; 3 ; 4 ; 5 ; 6. The need for proper uncertainty quantification in such calculations has recently been emphasized 7.scattering theoryelectron–atomcollisiontheoryscattering theory