In this article an introduction to the algebraic aspects of the Bethe
ansatz is given. The applications to the seminal spin 1/2 XXX model ar
e discussed in detail and the generalization to higher spin as well as
XXZ and the lattice sine-Gordon model are indicated. The origin of qu
antum groups and their appearance in CFT models are explained. The tex
t can be considered as a guide to the research papers in this field.