Dive into the first lecture of a comprehensive series on Numerical Relativistic Hydrodynamics, delivered by Kenta Kiuchi from the Albert Einstein Institute. Explore the fundamental concepts and mathematical foundations of this critical field in astrophysics, essential for modeling high-energy phenomena such as black hole and neutron star mergers, stellar collapses, and accretion processes. Gain insights into the intersection of General Relativity and magnetohydrodynamics, and understand how these numerical simulations contribute to interpreting gravitational wave signals and multi-messenger observations. Learn about the role of Numerical Relativity in modern astrophysics and its applications in upcoming gravitational wave, electromagnetic, and neutrino observatories.