This paper introduces the concept of topological crystalline insulators (TCIs), a new class of topological insulators that arise from the combination of time-reversal symmetry and crystal point group symmetry. Unlike conventional topological insulators, which rely on spin-orbit coupling, TCIs are characterized by surface states with quadratic band degeneracy protected by time-reversal and discrete rotational symmetry. These surface states appear on high symmetry crystal surfaces, such as the (001) face of a tetragonal crystal with C4 or C6 rotational symmetry. The paper presents a tight-binding model for a tetragonal crystal with C4 symmetry, showing that the (001) surface supports gapless surface states with quadratic band degeneracy. The topological nature of these states is characterized by a new Z2 topological invariant, which distinguishes between trivial and non-trivial phases. The invariant is defined using the symmetry properties of the Bloch wavefunctions and is shown to be gauge invariant. The paper also discusses the generalization of TCIs to crystals with C6 symmetry and highlights the importance of symmetry in protecting the topological properties of the surface states. The study shows that the surface states are robust against perturbations that break time-reversal or rotational symmetry. However, the presence of additional singlet surface bands may potentially disrupt the protection of the quadratic surface states. The paper concludes that TCIs represent a new class of topological insulators with potential applications in real materials.This paper introduces the concept of topological crystalline insulators (TCIs), a new class of topological insulators that arise from the combination of time-reversal symmetry and crystal point group symmetry. Unlike conventional topological insulators, which rely on spin-orbit coupling, TCIs are characterized by surface states with quadratic band degeneracy protected by time-reversal and discrete rotational symmetry. These surface states appear on high symmetry crystal surfaces, such as the (001) face of a tetragonal crystal with C4 or C6 rotational symmetry. The paper presents a tight-binding model for a tetragonal crystal with C4 symmetry, showing that the (001) surface supports gapless surface states with quadratic band degeneracy. The topological nature of these states is characterized by a new Z2 topological invariant, which distinguishes between trivial and non-trivial phases. The invariant is defined using the symmetry properties of the Bloch wavefunctions and is shown to be gauge invariant. The paper also discusses the generalization of TCIs to crystals with C6 symmetry and highlights the importance of symmetry in protecting the topological properties of the surface states. The study shows that the surface states are robust against perturbations that break time-reversal or rotational symmetry. However, the presence of additional singlet surface bands may potentially disrupt the protection of the quadratic surface states. The paper concludes that TCIs represent a new class of topological insulators with potential applications in real materials.