Aracne 2016. In this book we introduce some fundamental notions of Computability Theory, Decidability Theory, and Computational Complexity. We first consider the theory of computability based on Turing Machines and we illustrate how from simple devices one can build very powerful computational machines. We then present the theory of the Partial Recursive Functions. It provides an axiomatic characterization of the computable functions without referring to the notions of processor and memory.