Michael Powell is one of the world’s foremost figures in numerical analysis. This volume is derived from invited talks given at a meeting celebrating his 60th birthday and, reflecting Powell’s own achievements, focuses on innovative work in optimization and in approximation theory. The individual papers have been written by leading authorities in their subjects and are a mix of expository articles and surveys on new work. They have all been reviewed and edited to form a coherent volume that represents the state of the art in an important discipline within mathematics, with highly relevant applications throughout science and engineering.