This textbook, designed for senior undergraduates, or first year graduates in theoretical physics, introduces Einstein's General Relativity and Tensor Calculus, as well as important developments, such as: Black Holes were some time ago considered just a matter of imagination, devoid of reality, but we are now quite sure that they exist. These Black Holes are not far from us. They exist in the centre of galaxies not unlike our own. Mach's Principle was a name given by Einstein to the idea that inertia "here", is caused by the distant matter "there", in the whole Universe. Berman explores this subject, and includes the idea that the Universe has zero-total-energy. Based on this fact, the author extracted a series of conditions that need to be obeyed by the "Machian Universe" (read, "our" Universe). Variational methods are explored, including superpotentials, which provide simple energy calculations in General Relativity. Many of the topics presented in this book have never before appeared in literature for beginners in this subject.