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Evolutionary Algorithms, such as Evolution Strategies, Genetic Algorithms, or Evolutionary Programming, have found broad acceptance in the last ten years. In contrast to the broad propagation and the resulting practical prosperity in different scientific fields, the theory has not progressed as much. This monograph provides the framework and the first steps toward the theoretical analysis of Evolution Strategies (ES). The main emphasis is on understanding the functioning of these probabilistic optimization algorithms in real-valued search spaces by investigating the dynamical properties of some well-established ES algorithms on simple objective functions. The book introduces the basic concepts of such an analysis, such as the progress rate, the quality gain, and the self-adaptation response, and shows how to calculate these quantities. Based on this analysis, functioning principles are derived, aiming at a qualitative understanding of why and how ES algorithms do work.