The Geometry of Numbers is based on a book manuscript that Carl D. Olds, a New Zealand-born mathematician working in California at San Jose State University, was still writing when he died in 1979.
[1] The second part begins with Minkowski's theorem, that centrally symmetric convex sets of large enough area (or volume in higher dimensions) necessarily contain a nonzero lattice point.
After another chapter on the linear transformations of lattices, the book studies the problem of finding the smallest nonzero values of quadratic forms, and Lagrange's four-square theorem, the theorem that every non-negative integer can be represented as a sum of four squares of integers.
[6] However, reviewer Henry Cohn notes several copyediting oversights, complains about its selection of topics, in which "curiosities are placed on an equal footing with deep results", and misses certain well-known examples which were not included.
Despite this, he recommends the book to readers who are not yet ready for more advanced treatments of this material and wish to see "some beautiful mathematics".