This book presents a set of theoretical and experimental results that describe the features of the wide family of α-stable distributions (the normal distribution also belongs to this class) and their various applications in the mutation operator of evolutionary algorithms based on real-number representation of the individuals, and, above all, equip these algorithms with features that enrich their effectiveness in solving multi-modal, multi-dimensional global optimization problems. The overall conclusion of the research presented is that the appropriate choice of probabilistic model of the mutation operator for an optimization problem is crucial. Mutation is one of the most important operations in stochastic global optimization algorithms in the n-dimensional real space. It determines the method of search space exploration and exploitation. Most applications of these algorithms employ the normal mutation as a mutation operator. This choice is justified by the central limit theorem but is associated with a set of important limitations. Application of α-stable distributions allows more flexible evolutionary models to be obtained than those with the normal distribution. The book presents theoretical analysis and simulation experiments, which were selected and constructed to expose the most important features of the examined mutation techniques based on α-stable distributions. It allows readers to develop a deeper understanding of evolutionary processes with stable mutations and encourages them to apply these techniques to real-world engineering problems.