Based on lectures held at the Center for Theoretical Sciences in Taiwan in honor of Louis Nirenberg s 75th birthday, the volume contains both research papers dealing with various problems in Partial Differential Equations such as wave maps, the Navier-Stokes equations, and Lagrangian submanifolds. Professor Nirenberg is particularly appreciated for his generous encouragement of the development of mathematics in the Asia-Pacific region and the mixture of articles by distinguished mathematicians from Asia and other parts of the world.