This volume collects the expanded notes of four series of lectures given on the occasion of the CIME course on Nonlinear Optimization held in Cetraro, Italy, from July 1 to 7, 2007. The Nonlinear Optimization problem of main concern here is the problem n of determining a vector of decision variables x ? R that minimizes (ma- n mizes) an objective function f(-): R ? R, when x is restricted to belong n to some feasible setF? R, usually described by a set of equality and - n n m equality constraints: F = {x ? R: h(x)=0, h(-): R ? R; g(x) ? 0, n p g(-): R ? R }; of course it is intended that at...

These Lecture Notes arose from discussions we had over a working paper written by the first author in fall 1987. We decided then to write a short paper about the basic structure of evolutionary stability and found ourselves ending up with a book manuscript. Parts of the material contained herein were presented in a seminar at the Department of Mathematics at the University of Vienna, as well as at a workshop on evolutionary game theory in Bielefeld. The final version of the manuscript has certainly benefitted from critical comments and suggestions by the participants of both the seminar and...