Learn the fundamentals of parameter inference for gravitational wave sources in this comprehensive lecture from the Prospects in Theoretical Physics 2025 program at the Institute for Advanced Study. Explore the theoretical and computational methods used to extract physical parameters from gravitational wave detections, including techniques for analyzing signals from binary black hole mergers, neutron star collisions, and other astrophysical sources. Discover how Bayesian inference frameworks are applied to gravitational wave data analysis, examining the challenges of parameter estimation in the presence of noise and the statistical methods used to quantify uncertainties in measured parameters. Gain insights into the current state-of-the-art approaches for characterizing gravitational wave sources and understand how these techniques contribute to our understanding of fundamental physics and astrophysics through gravitational wave astronomy.