We give an elementary introduction to the theory of algebraic and topological
quantum groups (in the spirit of S. L. Woronowicz). In particular, we recall
the basic facts from Hopf (*-) algebra theory, theory of compact (matrix)
quantum groups and the theory of their actions on compact quantum spaces. We
also provide the most important examples, including the classification of
quantum SL(2)-groups, their real forms and quantum spheres. We also consider
quantum SL_q(N)-groups and quantum Lorentz groups.Comment: very small changes, will appear in Rev. Math. Phys., 46 pages, use
commands: csh intro.uu, tex intro (twice
