This review provides a pedagogical introduction to topological insulators (TIs), emphasizing basic theory and materials properties. It begins with a historical perspective, discussing the integer quantum Hall effect and the quantum spin Hall effect, which laid the groundwork for understanding TIs. The review highlights the discovery of TIs in 2D and 3D systems, focusing on the $ Z_2 $ topological classification and the role of time-reversal symmetry (TRS). It discusses the unique properties of TIs, such as their surface states and Dirac fermions, and how these properties lead to novel quantum phenomena. The review also covers the experimental verification of TIs, including the observation of gapless edge states and the quantization of conductance in quantum wells. It discusses the theoretical framework of topological field theory and the role of Dirac materials in TI research. The review concludes with a discussion of the $ Z_2 $ topological invariants in 3D systems and their implications for the classification of TIs. Key concepts include the bulk-boundary correspondence, the role of Berry phase, and the significance of TRS in protecting the topological surface states of TIs. The review emphasizes the importance of transport measurements in identifying and characterizing TI materials.This review provides a pedagogical introduction to topological insulators (TIs), emphasizing basic theory and materials properties. It begins with a historical perspective, discussing the integer quantum Hall effect and the quantum spin Hall effect, which laid the groundwork for understanding TIs. The review highlights the discovery of TIs in 2D and 3D systems, focusing on the $ Z_2 $ topological classification and the role of time-reversal symmetry (TRS). It discusses the unique properties of TIs, such as their surface states and Dirac fermions, and how these properties lead to novel quantum phenomena. The review also covers the experimental verification of TIs, including the observation of gapless edge states and the quantization of conductance in quantum wells. It discusses the theoretical framework of topological field theory and the role of Dirac materials in TI research. The review concludes with a discussion of the $ Z_2 $ topological invariants in 3D systems and their implications for the classification of TIs. Key concepts include the bulk-boundary correspondence, the role of Berry phase, and the significance of TRS in protecting the topological surface states of TIs. The review emphasizes the importance of transport measurements in identifying and characterizing TI materials.