  This survey is based on a series of five lectures, given May 3--7, 2010, at
the Centre de Recerca Matematica, Barcelona. The goal of the lectures was to
present aspects of the theory of foliation dynamical systems which have
particular importance for the classification of foliations of compact
manifolds. The lectures emphasized intuitive concepts and informal discussion,
while taking the reader into topics of active research in this subject. These
notes update and expand on the lectures, and include more recent progress. This
article also includes an extensive set of references, as well as highlighting
many open questions and problems. A set of "homework problems" is also
included, one for each day of lecture.
