This book is about spin systems as models for magnetic materials, especially antiferromagnetic lattices. Spin-systems are well-defined models, for which, in special cases, exact properties may be derived. These special cases are for the greater part, one- dimensional and restricted in their applicability, but they may give insight into general properties that also exist in higher dimension. This work pays special attention to qualitative differences between spin lattices of different dimensions. It also replaces the traditional picture of an (ordered) antiferromagnetic state of a Heisenberg system by one which makes use of the space of quantum spin states.Contents: IntroductionSpin systems as models for magnetic materialsQuantum mechanics of spinsDifferent types of interaction Model HamiltoniansExact results for one-dimensional systemsGeneral survey of results in one and two dimensionsState of art for three-dimensional systemsRecent developmentsReadership: Theoretical solid-state physicists.Key Features:A self-contained and integrated monograph — both algorithms and applications are included; mathematical foundations and principles are discussedMost recent advances and innovations on ecological applications of graphs, networks and agent-based modeling are includedJava codes and a standalone software package are presented for easy use by readersA large number of examples are provided