1 -- The Coin-Exchange Problem of Frobenius -- A Gallery of Discrete Volumes -- Counting Lattice Points in Polytopes:The Ehrhart Theory -- Reciprocity -- Face Numbers and the Dehn--Sommerville Relations in Ehrhartian Terms -- Magic Squares -- 2 -- Finite Fourier Analysis -- Dedekind Sums, the Building Blocks of Lattice-point Enumeration -- The Decomposition of a Polytope into Its Cones -- Euler--Maclaurin Summation in ́ -- Solid Angles -- A Discrete Version of Green's Theorem Using Elliptic Functions