This book presents a comprehensive review of the methods applied to derive cosmological parameters for a given model and test different cosmological models using the most massive collapsed structures in our Universe: clusters of galaxies. Clusters typically consist of hundreds of galaxies and high-temperature ionized gas trapped in their gravitational field dominated by dark matter extending out to 2-3 Mpc. The formation, evolution, and structure of these massive rare objects are sensitive probes of the assumed cosmology. This is a multidisciplinary field of astrophysics involving multi-wavelength observations, gravity theory, atomic physics, plasma physics, magneto-hydrodynamics, astrophysical cosmology and numerical simulations. Our understanding of the physics of clusters, which is essential when using them for cosmology, has been improved tremendously due to the recent advent of technology and observational strategy in multi-frequency observations, and enhanced by improved numerical simulations made possible by more advanced high performance computers. As a result of these developments, cosmology with clusters of galaxies has become a mature discipline recently, and provided an important contribution to establish our concordance cosmological constant dominated cold dark matter model. In the near future we expect a rapid expansion of this field due to results from new cluster surveys and multi-wavelength observations. This timely volume on this exciting newly established field discusses galaxy cluster physics and provides a detailed description of using clusters to derive cosmological parameters applying accurate measurements of individual clusters as well as using clusters as a statistical tool. A detailed discussion is given on degeneracies between derived parameters and the systematic effects, which are becoming a limiting factor. An account for using clusters to test different cosmological models is also presented. This volume provides an introduction to galaxy cluster cosmology for physics and astronomy graduate students and serves as a reference source for professionals.