INTRODUCTION TO QUANTUM GROUPS

We give an elementary introduction to the theory of algebraic and topo logical quantum groups tin the spirit of S. L. Woronowicz). In particu lar, we recall the basic facts from Hopf (-) algebra theory, theory o f compact (matrix) quantum groups and the theory of their actions on c ompact quantum spaces. We also provide the most important examples, in cluding the classification of quantum SL(2)-groups, their real forms a nd quantum spheres. We also consider quantum SLq(N)-groups and quantum Lorentz groups.