In his foreword to Santalo´’s treatise (1976), partly quoted as a motto to this chapter, Mark Kac pointed out a need for a measure-theoretic formulation of probability theory in general, and random geometry in particular. We shall therefore initially devote some space to one of Bertrand’s paradoxes, and thus motivate the formulation of random geometry as it was accomplished in the first half of the twentieth century. This will set the stage for a review of some basic notions of classical probability theory of engineering and applied science curricula, as well as for an introduction to the simplest random geometric models of disordered microstructures. The review is not completefor instance, the conditional probability and description of microstructures by joint probability distributions are not treated. The focus of this chapter is on a review of basic concepts of random processes and fields for discrete systems.