Branes are solitonic configurations of a string theory that are represented by extended objects in a higher-dimensional space-time. They are essential for a comprehension of the non-perturbative aspects of string theory, in particular, in connection with string dualities. From the mathematical viewpoint, branes are related to several important theories, such as homological mirror symmetry and quantum cohomology. Geometry and Physics of Branes provides an introduction to current research in some of these different areas, both in physics and mathematics. The book opens with a lucid introduction to the basic aspects of branes in string theory. Topics covered in subsequent chapters include tachyon condensation, the geometry surrounding the Gopakumar-Vafa conjecture (a duality between the SU(N) Chern-Simons theory on S3 and a IIA string theory compactified on a Calabi-Yau 3-fold), two-dimensional conformal field theory on open and unoriented surfaces, and the development of a homology theory naturally attached to the deformations of vector bundles that should be relevant to the study of homological mirror symmetry.