Explore the mechanisms of evolution in this comprehensive lecture on population genetics and evolution. Delve into key concepts such as the Long-Term Evolution Experiment (LTEE) on E. coli, adaptation to citrate, and simple exponential growth. Examine the Galton-Watson process, including its continuous time version and generating functions. Investigate the logistic function, selection in continuous time, and frequency-dependent selection. Learn about measuring fitness in the LTEE and positive selection. Conclude with an exploration of the prisoner's dilemma in an RNA virus. Gain valuable insights into evolutionary processes and their applications in modern biology through this in-depth presentation by Luca Peliti at the International Centre for Theoretical Sciences.