Einstein's Space-Time: An Introduction to Special and General Relativity is a textbook addressed to students in physics and other people interested in Relativity and a history of physics. The book contains a complete account of Special Relativity that begins with the historical analysis of the reasons that led to a change in our manner of regarding the space and time. The first chapters are aimed to afford a deep understanding of the relativistic spacetime and its consequences for Dynamics. The chapter about covariant formulation includes among its topics the concepts of volume and hypersurfaces in manifolds, energy-momentum tensor of a fluid, and prepares the language for General Relativity. The last two chapters are devoted to an introduction of General Relativity and Cosmology in a modern approach connected with the latest discoveries in these areas.