This is an introductory approach to the electron-atom scattering theoretical formulation. It focuses on the mathematical tools and on the physics underlying the modern description of electrons, atoms, and electron-atom scattering. It is organised into four parts each divided into two chapters. Chapter headings: The Fundamental Equations; The General Formalism; Atoms; Elastic and Inelastic Scattering; Relativistic Equations; Quantum-Relativistic Scattering; Electrons Impinging on Solids; The Monte Carlo Simulations.