Explore entropy techniques for analyzing nonlinear partial differential equations in this comprehensive lecture by Tony Lelievre. Delve into the power of these methods in studying the long-term behavior of solutions to nonlinear PDEs, with a focus on their application to Fokker-Planck equations associated with nonlinear stochastic differential equations in the McKean sense. Examine the fundamental role of logarithmic Sobolev inequalities in these techniques. Discover practical applications through three key examples: micro-macro models for polymeric fluids, adaptive biasing force techniques for molecular dynamics, and optimal scaling for high-dimensional Metropolis-Hastings algorithms. Gain valuable insights from this presentation, which was part of the Hausdorff Trimester Program on Optimal Transportation and its Applications.