Delve into the fourth lecture of a comprehensive series on the theory and numerical methods for partial differential equations, delivered by Harald Pfeiffer at the International Centre for Theoretical Sciences. Explore advanced concepts in numerical relativity as part of a two-week summer school on gravitational-wave astronomy. Gain insights into the mathematical foundations and computational techniques essential for modeling complex astrophysical phenomena such as black hole mergers, neutron star collisions, and stellar collapses. Enhance your understanding of the crucial role numerical simulations play in interpreting gravitational-wave signals and advancing our knowledge of high-energy astrophysics.