This review provides a pedagogical overview of the fundamental concepts, basic theories, expected properties, and material realizations of topological superconductors. It emphasizes the relationship between topological superconductivity and Majorana fermions, distinguishing between dispersive Majorana fermions and localized Majorana zero modes. The review covers various routes to topological superconductivity, highlighting the role of spin-orbit coupling. It also summarizes the current experimental situations and possible signatures of topological superconductivity, focusing on intrinsic topological superconductors. The content is structured into several sections, including an introduction to topology in quantum mechanics, the basics of superconductivity, the theory of topological superconductors, the role of symmetry, and the properties of topological superconductors. The review concludes with an outlook and acknowledgments.This review provides a pedagogical overview of the fundamental concepts, basic theories, expected properties, and material realizations of topological superconductors. It emphasizes the relationship between topological superconductivity and Majorana fermions, distinguishing between dispersive Majorana fermions and localized Majorana zero modes. The review covers various routes to topological superconductivity, highlighting the role of spin-orbit coupling. It also summarizes the current experimental situations and possible signatures of topological superconductivity, focusing on intrinsic topological superconductors. The content is structured into several sections, including an introduction to topology in quantum mechanics, the basics of superconductivity, the theory of topological superconductors, the role of symmetry, and the properties of topological superconductors. The review concludes with an outlook and acknowledgments.