In this chapter we recapitulate basic results of geometric and analytic theory of numbers (for more details the reader is referred to G.H. Hardy, E.M. Wright [1958], F. Fricker [1982], E. Hlawka et al. [1991], E. Kra¨tzel [2000], and many others). Our intent is twofold: on the one hand, known key information of analytic number theory should be provided as preparation; on the other hand, the material should serve as an appropriate reference for our later work on lattice point summation.