This book is the Proceedings of the Workshop/Conference on Geometry and Topology which was held at the Indian Institute of Technology, Bombay, August 2007. There are two parts in it. Part consists of notes from four mini-courses presented by

(i) Professor K. Y. Lam (Univ. Br. Columbia) on Topological Methods in the Theory of Bilinear Forms

(ii) K. Varadarajan (Univ. Calgary), on The Wall Finiteness Obstruction (iii) P. Wong (Bates College, Maine), on Combinatorial and Geometric Group Theoretic
Methods in Fixed Point Theory and

(iv) P. Zvengrowski (Univ. of Calgary) on An Introduction to I-Homology. The material in these four mini courses encompassed a broad spectrum of important, up-to-date and deep parts of classical and modern algebraic topology, along with related areas in other parts of mathematics such as algebra, geometry, number theory, analysis, and applied mathematics (e.g. the theory of elasticity). There are remarkably many interconnections between the four mini courses.

Part II consists of selected papers presented in the Conference by some of the most distinguished people in the field. The topics range over a broad spectrum, from theoretical physics to topology, geometry, algebra, etc., and include reports about some of the most recent important developments in the field such as the recent solution of the Poincaré Conjecture by Pereleman et al., to name just one example. These papers also represent the interplay of modern algebraic topology with algebraic geometry, algebraic groups, differential geometry, and non-commutative geometry. We feel that the volume will have a lasting value for students and researchers in the specific areas that are covered.