The general theory of relativity, also called the Einstein's theory of gravity and the general relativity theory, is the geometric theory of gravitation. It provides the description of gravity as a geometric property of space and time. There are several astrophysical applications of the general theory of relativity including gravitational lensing, cosmology, gravitational-wave astronomy, and black holes. The theory of general relativity forms the basis for disciplines of cosmology and relativistic astrophysics. Cosmology is a branch of astronomy that studies the origin and evolution of the universe. The contemporary researches in cosmology are based on the field equations of general relativity. Under cosmology, the universe is considered on extremely large scales that are evolving over extremely long times that are comparable to the age of the universe. Some researchers have also proposed cosmological models based on space-times with dimensions, D > 4. Some of the important applications of general relativity in cosmology and astrophysics include gamma-ray bursts, neutron stars, black holes and gravitational waves. This book includes some of the vital pieces of works being conducted across the world, on various topics related to modern general relativity. Researchers and students studying this theory and its applications will be assisted by this book.