This chapter is devoted to Furstenberg’s multiple recurrence result, yielding, via Furstenberg’s correspondence principle, an ergodic theoretic proof of Szemerdi’s theorem on arithmetic progressions in large sets of integers. The first proof of multiple recurrence in this book follows the classical proof due to Furstenberg, Katznelson and Ornstein based on the FurstenbergZimmer structure theorem, where we employ the abstract approach by Tao. Here, we use a stronger statement than the dichotomy between compact and weakly mixing extensions in one of the steps, namely the conditional Jacobsde LeeuwGlicksberg decomposition. Then we very briefly discuss a second proof based on the original approach of Furstenberg using distal factors of finite order. Two more proofs of multiple recurrence follow in Chap. 15 . We finish with an overview of some further developments.