This book is intended to serve as a textbook for undergraduate and postgraduate students of mathematics. It will be useful to the researchers working in the field of differential geometry and its applications to the general theory of relativity and other applied areas. It will also be helpful in preparing for competitive examinations like IAS, IES, NET, PCS, and other higher education tests. The text starts with the basic concepts and results, which shall refer throughout this book and is followed by the study of the tensor algebra and its calculus, consisting the notion of tensor, its operations, and its different types; Christoffels symbols and its properties, the concept of covariant differentiation of tensors and its properties, tensor form of the gradient, divergence, Laplacian and curl the divergence of a tensor, intrinsic derivatives, and parallel displacement of vectors, Riemann's symbols and its properties, and application of tensor in different areas.
