For more than a century, our understanding of gravitational physics has been based on Albert Einstein's theory of general relativity (GR). Einstein's theory fundamentally changed our understanding of the universe, its origin and evolution. General relativity accurately describes many phenomena occurring on very distinct scales. However, most of the GR-compatible observational and experimental results fall within the gravitational weak-field regime. In recent years, discrepancies between the data and the corresponding general relativity predictions have been observed and have generated intense research activity. One of the most critical aspects of general relativity refers to the presence of singularities in extreme physical situations. These discrepancies indicate that either general relativity needs to be modified in the regime of strong-field gravity and large spacetime curvature, or the parameters of the theory should be modified. In this book we concentrate our attention to the best astrophysical laboratories to probe strong-field gravity: black holes and neutron stars. We also discuss extensions of general relativity that encompass the quantum universe.
