  Affine quantum groups are certain pseudo-quasitriangular Hopf algebras that
arise in mathematical physics in the context of integrable quantum field
theory, integrable quantum spin chains, and solvable lattice models. They
provide the algebraic framework behind the spectral parameter dependent
Yang-Baxter equation.
  One can distinguish three classes of affine quantum groups, each leading to a
different dependence of the R-matrices on the spectral parameter: Yangians lead
to rational R-matrices, quantum affine algebras lead to trigonometric
R-matrices and elliptic quantum groups lead to elliptic R-matrices. We will
mostly concentrate on the quantum affine algebras but many results hold
similarly for the other classes.
  After giving mathematical details about quantum affine algebras and Yangians
in the first two section, we describe how these algebras arise in different
areas of mathematical physics in the three following sections. We end with a
description of boundary quantum groups which extend the formalism to the
boundary Yang-Baxter (reflection) equation.
