In this book I present differential geometry and related mathematical topics with the help of examples from physics. It is well known that there is something strikingly mathematical about the physical universe as it is conceived of in the physical sciences. The convergence of physics with mathematics, especially differential geometry, topology and global analysis is even more pronounced in the newer quantum theories such as gauge field theory and string theory. The amount of mathematical sophistication required for a good understanding of modern physics is astounding. On the other hand, the philosophy of this book is that mathematics itself is illuminated by physics and physical thinking
