Book excerpt: This book presents a self-contained introduction to the theory of minisum hyperspheres. This specialized research area within the larger field of geometric optimization is full of interesting and open problems. This work provides an overview of the history of minisum hyperspheres as well as describes the best techniques for developing and solving minisum hypersphere problems. Various related areas of geometric and nonlinear optimization are also discussed. As the first publication devoted to this area of research, this work will be of great interest to graduate-level researchers studying minisum hypersphere problems as well as mathematicians interested geometric optimization.