Abstarct: One of the challenges for scientists is finding an answer to the question of how to obtain the effective Hamiltonian of a given system in a completely principled way. To investigate this process, we first start with calculating the band structure using first-principles calculations, and then we proceed to find the relationship between the tight-binding approximation and Slater and Koster integrals. The results of these calculations determine the elements of the Hamiltonian matrix and the overlap matrix between different orbitals in the nonlinear baxses. Next, using the Levenberg-Marquardt method as one of the best nonlinear fitting techniques, we will fit the band structure obtained from first-principles methods to the band structure derived from the tight-binding approximation. This process leads to the calculation of the tight-binding model parameters and the on-site energies. The explanations provided are baxsed on the principles of operation of the tight-binding software, TBStudio. This software is used for discovering the tight-binding Hamiltonian of low-dimensional structures, particularly in the design and development of two-dimensional materials. After establishing the computational infrastructure in this software, we will calculate and examine the electronic properties of topological two-dimensional structures using first-principles methods. Initially, our focus in this thesis is on calculating the tight-binding Hamiltonian of topological insulators BiTeX. Subsequently, in the tight-binding model for the studied structures, the Slater and Koster coefficients were calculated. We also obtained the on-site energies of the atoms and the electronic transfer integrals between different orbitals for the studied system, along with the overlap matrices. Using the calculated Hamiltonian, we can extract and examine the band structure properties, including electrical characteristics and other computable properties through Green's function calculations. Additionally, using the calculated two-dimensional Hamiltonian, we obtained the Hamiltonian for the nanoribbons of the studied structure and investigated their band structure and transport properties.