Explore the intriguing concept of wave dark matter in this comprehensive lecture delivered by Hyungjin Kim at the Galileo Galilei Institute. Delve into the latest theories and research surrounding this fascinating aspect of cosmology, examining how wave properties could potentially explain the behavior and distribution of dark matter in the universe. Gain insights into the mathematical models, observational evidence, and potential implications for our understanding of galactic structure and cosmic evolution. Engage with cutting-edge ideas at the intersection of quantum mechanics and astrophysics, and discover how wave dark matter might resolve longstanding puzzles in modern cosmology.