This book introduces students in their early semesters to the exciting and challenging aspects of relativity theory and modern cosmology, while also providing plenty of new material for advanced learners and researchers. The book's particular strength lies in its emphasis on the fundamental, logical, and geometric aspects of the theory. It covers both special and general relativity in conjunction with current developments in cosmology. Another distinctive feature is the prioritization of intuition and understanding over mathematical formalism: only after consolidating the acquired knowledge is it translated into a mathematical, manageable form. The book includes numerous exercises and serves as an excellent supplementary reading for lectures.