This part of the book develops results and themes from the course and in doing so presents several strands of research in dynamics. The exposition relies on and refers to the course, but it stands on its own as a careful description of selected modern achievements. The choice of subjects was influenced by the topics of the course and the degree to which these results have been digested in the literature.

Starting with Chapter 10, we adopt a style less technically thorough than that of the course. Many results come with at least a proof outline, but not all arguments labeled as proofs are as complete and self-contained as in the course. The focus is on making clear how ideas are elaborated and used. Many references are given in the text.

The chapters are largely independent of each other, and can be read selectively and in any order.