The natural domain for a convex function is a convex set. In this chapter we review some basic facts, necessary for a deep understanding of the concept of convexity in real linear spaces. For reader’s convenience, all results concerning the separation of convex sets in Banach spaces are stated in Section 2.2 with proofs covering only the particular (but important) case of Euclidean spaces. Full details in the general case are to be found in Appendix  B