ABSTRACT
In this chapter we introduce several notions and results from polyhedral geometry, combinatorial optimization and linear programming. Excellent general references for these areas are [35, 87, 281, 372, 373, 438]. Then we study relative volumes of lattice polytopes. We present various relations between Hilbert bases, TDI linear systems of inequalities, the max-flow mincut property of clutters, integral linear systems, and the normality of affine semigroups and Rees semigroups. Elementary integral vectors and matroids are introduced at the end of the chapter.
