This book 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.The first part is devoted to the fundamentals of quantum mechanics, i.e. the Schrodinger equation, the Heisenberg uncertainty principle and the general formalism. The second part concerns the many electron atoms and introduces the scattering of electrons. The third part is devoted to the quantum relativistic theory of the electron and of the electron-atom elastic scattering. The fourth part concerns selected aspects of the interaction of electrons with the matter: absorption, backscattering, transmission, depth distribution of the absorbed electrons, energy and angular distribution of the backscattered electrons, and secondary electrons.