This course covers the Graph Minors project of Robertson and the speaker, and related topics. Two highlights of this are: (a) in any infinite set of graphs, one of them is a minor of another, and (b) the k vertex-disjoint paths problem in graphs is solvable in polynomial time, for all fixed k. On the way we cover graph path-width and tree-width, graph well-quasi-ordering, containment relations and some structure theorems for tournaments, and other topics as time permits.