The purpose of this book is to give a quick introduction to the theory of foliations,
as well as to Lie groupoids and their infinitesimal version – Lie algebroids.
The book is written for students who are familiar with the basic concepts of
differential geometry, andall the results presentedin this book are provedin
detail.
The topics in this book have been chosen so as to emphasize the relations
between foliations, Lie groupoids and Lie algebroids. Lie groupoids form the
main tool for the study of the ‘transversal structure’ (the space of leaves) of
a foliation, by means of its holonomy groupoid. Foliations are also a special
kindof Lie algebroids. At the same time, the elementary theory of foliations is
a very useful tool in studying Lie groupoids and Lie algebroids.