The main objective of these lecture notes is to provide basic notions about the finite element discretization of frictionless contact in elastodynamics, to point out where the main problems may occur, and what are the possible remedies. They suppose a basic knowledge of elastodynamics and of the finite element method. It is also recommended to have some notions about unilateral contact in elastostatics (the so-called Signorini problem). They cover only frictionless contact, for the sake of simplicity.