An ontology of continuants and occurrents to be developed in the course of the book within a framework of regions of space and intervals of time is initially outlined in this chapter. First and foremost, quantities of matter, to which the principles of classical mereology are held to apply, are distinguished from material objects, here called individuals, that change their constitutive matter over time and to which mereological principles don’t apply. The motivation for this and detailed development of the features of the constitutes relation (as distinct from mereological parthood) comes in Chaps. 2 and 3 . On this understanding, certain lines of objection to classical principles of mereology are put aside. Rehearsing reasons for rejecting some other suggestions for modifying classical principles mereology serves further to illustrate how the mereological concepts are understood here. But the main thrust of the chapter is to emphasise what the mereological principles say and what they leave open concerning the relations of part, overlap, separation and identity and the operations of sum, product and difference. Classical mereology is an incomplete theory whose axioms can be supplemented in various ways to characterise the kind of objects to which they apply. It is shown how this can be done for a theory reasonably called a theory of temporal intervals and again, when supplemented with an additional, nonmereological, primitive, to develop a theory of spatial regions. Both theories are complete first order theories (i.e., no further independent axioms can be added without contradiction). An analogous development doesn’t seem feasible for a pure mereological theory of quantities of matter. Developing a theory of quantities of matter requires introducing times and spaces, as well as other entities, along with predicates relating these various kinds of entities—a project pursued in the following chapters. Readers who are not interested in the technical details may like to skim quickly over the presentations of the theories of times and spaces, together with the proof of completeness, in Sects. 1.3 and 1.4 and their corresponding subsections, and proceed directly to the final section of the chapter which outlines the strategy for the remainder of the book.