To study the representations of a complex connected semisimple algebraic group G, one usually chooses a Borel subgroup B in G and a maximal torus T contained in B. Given a representation of G on a vector space V, it is thus natural to look at the bases of V that are compatible with this choice of (B,T). Works by Zelevinsky, Berenstein, Lusztig and Kashiwara led to the notions of " canonical basis ", " good basis ", " perfect basis ", " string basis ", ... , and to the construction of such bases. The aim of this memoir is to provide a short introduction to this theory and to present some remarkable properties of these bases and of the combinatorics they define.
