Genetic Algorithms (GA), which are based on the idea of optimizing by simulating the natural processes of evolution, have proven successful in solving complex problems that are not easily solved through conventional methods. This chapter introduces their major steps, operators, theoretical foundations, and problems. A parallel GA is an extension of the classical GA that takes advantage of a GA’s inherent parallelism to improve its time performance and reduce the likelihood of premature convergence. An overview of different models for parallelizing GAs is presented along with a discussion of their main advantages and disadvantages. A case study: A parallel GA for finding Ramsey Numbers is then presented. According to Ramsey Theory, a sufficiently large system (no matter how random) will always contain highly organized subsystems. The role of Ramsey numbers is to quantify some of these existential theorems. Finding Ramsey numbers has proven to be a very difficult task that has led researchers to experiment with different methods of accomplishing this task. The objective of the case study is both to illustrate the typical process of GA development and to verify the superior performance of parallel GAs in solving some of the problems (e.g., premature convergence) of traditional GAs.