Nesterov (Center of Operations Research and Econometrics, Universitè Catholique de Louvain, Belgium) explains the main ideas of complexity theory for convex optimization, covering optimal methods and lower complexity bounds for smooth and non-smooth convex optimization. A separate chapter is devoted to polynomial-time interior-point methods. An undergraduate background in analysis and linear algebra is assumed. The book can be used for a one-semester course, and will be useful for industrial engineers and economists.