The methodological approach we will adopt is quantitative in two respects: on one hand, we will consider quantities (the computational resources) on the concrete level of actually performing a computation; on the other hand, we will adopt quantities in reasoning about computation, e.g. for tasks like the analysis and verification of various (both qualitative and quantitative) programs properties. A particular role is played by probabilities which allow us to address problems which are beyond the scope of many traditional methods.