Simple Genetic Algorithms (SGAs) are used in science and engineering as adaptive algorithms for solving practical problems and as computational models of natural evolutionary systems. The book focuses on Simple Genetic Algorithm as an evolutionary system, enabling the reader to be goal-oriented while exploring topics in mathematics and computer science. The primary aim of this text is to provide an introduction to what is known (and proven) about the theory of Simple Genetic Algorithm. The rigor of mathematics is employed so as to not to inadvertently repeat myths or recount folklore. The second objective is to make available algorithms for the computation of mathematical objects related to SGA. The text stresses on theoretical foundations upon which provable results about SGA behaviour can be based.