We give an elementary introduction to the Drinfeld-Jimbo procedure of the quantum deformation Uq(g) of semisimple Lie algebras g. The q—Serre relations are discussed in some detail, in the Chevalley and the Cartan—Weyl basis. We review the real forms of g and Uq(g). The general procedure is illustrated by the examples Uq(sℓ(2)) and Uq (so(5, ℂ)). After some general considerations on non-semisimple Lie algebras, we discuss in detail the quantum deformation of the Poincaré algebra, involving the contraction of Uq(so(3, 2)). Some physical consequences are mentioned.