These notes correspond rather accurately to the translation of the lectures given at the Fifth Mexican School of Particles and Fields, held in Guanajuato, Gto., in December 1992. They constitute a brief and elementary introduction to quantum symmetries from a physical point of view, along the lines of the forthcoming book by C. Go´mez, G. Sierra, and myself: 1) Introduction. 2) Factorizable S‐matrices. 3) Bethe’s diagonalization of spin chain hamiltonians. 4) Integrable vertex models: the six‐vertex model. 5) The Yang‐Baxter algebra. 6) Physical spectrum of the Heisenberg spin chain. 7) Yang‐Baxter algebras and braid groups. 8) Yang‐Baxter algebras and quantum groups. 9) Affine quantum groups. 10) Hopf algebras. 11) The quantum groupUq(G). 12) Comments. 13) References. © 1994American Institute of Physics