This talk gives an elementary introduction to some recent work on 
arithmetic progression and summarizes some of the topics discussed at 
the recent Oberwolfach Arbeitsgemeinschaft "Ergodic Theory and 
Combinatorial Number Theory". 

The talk includes a more detailed discussion of a result of Hillel 
Furstenberg and Benji Weiss which produces monochromatic binary subtrees 
of colored trees, generalizing van der Waerden's theorem and Szemeredi's 
theorem.