  These are the notes of a series of lectures delivered by the author at the
Graduate School of Mathematics of the University of Tokyo, during the month of
October 2015. They were meant to be as self-contained as possible, taking into
account time and space. The basic idea was to introduce the concepts and some
of the basic results in the theory of holomorphic foliations with
singularities. Another goal is to guide the reader to some of the recent
questions and problems in the field, providing in this way a motivating
introduction to those who are interested in studying a new subject.
