Dive into the first lecture of a comprehensive series on the theory and numerical methods for partial differential equations. Explore fundamental concepts and techniques essential for understanding and solving complex mathematical problems in physics and engineering. Learn from Harald Pfeiffer, an expert from the Albert Einstein Institute, as he introduces key principles and lays the groundwork for advanced topics in numerical relativity and gravitational wave astronomy. Gain valuable insights into the mathematical foundations crucial for modeling high-energy astrophysical phenomena and interpreting gravitational wave signals from cosmic events.