This book describes Carmelis cosmological general and special relativity theory, along with Einsteins general and special relativity. These theories are discussed in the context of Moshe Carmelis original research, in which velocity is introduced as an additional independent dimension. Four- and five-dimensional spaces are considered, and the five-dimensional braneworld theory is presented. The TullyFisher law is obtained directly from the theory, and thus it is found that there is no necessity to assume the existence of dark matter in the halo of galaxies, nor in galaxy clusters. The book gives the derivation of the Lorentz transformation, which is used in both Einsteins special relativity and Carmelis cosmological special relativity theory. The text also provides the mathematical theory of curved space­time geometry, which is necessary to describe both Einsteins general relativity and Carmelis cosmological general relativity. A comparison between the dynamical and kinematic aspects of the expansion of the universe is made. Comparison is also made between the FriedmannRobertsonWalker theory and the Carmeli theory. And neither is it necessary to assume the existence of dark matter to correctly describe the expansion of the cosmos.