This chapter deals with various types of elastic scattering interactions that heavy and light charged particles can have with atoms of an absorber. The interactions fall into the general category of Coulomb interactions and the chapter starts with a discussion of the intriguing Geiger-Marsden experiment of alpha particle scattering on thin gold foils. The experiment is of great historical importance and its results have lead to Rutherford’s ingenious conclusion that most of the atom is empty space and that most of the atomic mass is concentrated in the atomic nucleus. The kinematics of the α particle scattering is discussed in detail and the differential and total cross section concept for scattering is introduced for Rutherford scattering and expanded to other types of Coulomb scattering.