In the early part of the 20th century, Hermann Minkowski developed a novel geometric approach to several questions in number theory. This approach developed into a field called the geometry of numbers and it had an influence on fields outside number theory as well, particularly functional analysis and the study of Banach spaces, and more recently on cryptography and discrete optimization. This chapter covers those aspects of the geometry of numbers that are most relevant for the second part of the book on optimization. Topics include the basic theory of lattices (including Minkowski’s convex body theorem), packing and covering radii, shortest and closest lattice vector problems (SVPs and CVPs), Dirichlet-Voronoi cells, Khinchine’s flatness theorem, and maximal lattice-free convex sets. Several topics like lattice basis reduction and SVP/CVP algorithms are presented without making a rationality assumption as is common in other expositions. This presents a slightly more general perspective on these topics that contains the rational setting as a special case.