Books in the Chicago Lectures in Mathematics series

This work seeks to offer a concise introduction to geometric group theory - a method for studying infinite groups via their intrinsic geometry. Basic combinatorial and geometric group theory is presented, along with research on the growth of groups, and exercises and problems.

Provides a treatment of algebraic topology that reflects the enormous internal developments within the field and retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented.

The theorems of Marina Ratner have guided key advances in understanding dynamical systems. Here, the author offers an introduction to these theorems and an account of the proof of Ratner's measure classification theorem. This is a collection of lecture notes aimed at graduate students and brings these theorems to a broader mathematical readership.

With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. This title addresses the course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. It covers topics that are useful for algebraic topologists.

This study presents the results of the authors' development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms.