The course notes of an algebraic multigrid course for graduate and PhD students at the University of Heidelberg are now available.

The discussed algebraic multigrid approaches are classified into several groups. One or two representatives of these groups are analyzed in detail, while the other members of these classes are briefly summarized. Theoretical and numerical results are presented.

The selection of the algorithms is not assumed to be complete and does not induce any rating of the performance of algebraic multigrid methods.