In this chapter we present transformation semigroups and their applications. We begin with Klein’s approach to geometry based on invariants of transformation groups. Then, we present symmetry groups in chemistry and in classical mechanics. Next we introduce one-parameter semigroups of transformations and their applications in ergodic theory. Our main subject are one-parameter semigroups of operators, in particular stochastic semigroups. We present general results on their existence and long-time behavior. We also give examples of one-parameter semigroups related to Markov chains, diffusion, and processes with jumps. We focus on the applications of semigroups of operators in biology. Among other things, we study models of DNA evolution; growth of erythrocyte population; gene expression; cell cycle; and the movement of bacteria and insects. We also consider models with stochastic noise and different population models.