Topological insulators are a class of materials characterized by unique quantum mechanical properties, particularly the presence of gapless edge or surface states due to the topological nature of their bulk wave functions. This review provides a pedagogical introduction to the field, focusing on the basic theory and material properties. It covers the historical perspective, including the discovery of the integer quantum Hall effect and the quantum spin Hall effect, and discusses the theoretical developments leading to the understanding of topological phases. The review also delves into the characterization of topological insulators using transport measurements, the concept of Berry phase, and the $Z_2$ topological invariant. It explains how these concepts are applied to understand the properties of 2D and 3D topological insulators, including the Dirac fermion physics and quantum oscillation patterns. The review concludes by discussing the prospects of topological insulators for exploring novel quantum phenomena.Topological insulators are a class of materials characterized by unique quantum mechanical properties, particularly the presence of gapless edge or surface states due to the topological nature of their bulk wave functions. This review provides a pedagogical introduction to the field, focusing on the basic theory and material properties. It covers the historical perspective, including the discovery of the integer quantum Hall effect and the quantum spin Hall effect, and discusses the theoretical developments leading to the understanding of topological phases. The review also delves into the characterization of topological insulators using transport measurements, the concept of Berry phase, and the $Z_2$ topological invariant. It explains how these concepts are applied to understand the properties of 2D and 3D topological insulators, including the Dirac fermion physics and quantum oscillation patterns. The review concludes by discussing the prospects of topological insulators for exploring novel quantum phenomena.