This paper introduces the concept of "topological crystalline insulators," which are three-dimensional materials with metallic surface states characterized by quadratic band degeneracy on high-symmetry crystal surfaces. These materials are the counterpart of topological insulators in materials without spin-orbit coupling, where electron orbital degrees of freedom play a role similar to spin. The authors extend the topological classification of band structures to include crystal point group symmetries, specifically focusing on four-fold ($C_4$) and six-fold ($C_6$) rotational symmetries. They introduce a new $\mathbb{Z}_2$ topological invariant to characterize the band structures of these materials, which is crucial for understanding their topological stability and the existence of gapless surface states. The paper also discusses the electronic properties of these surface states and provides a tight-binding model to illustrate the formation of gapless surface states on the (001) surface. The authors conclude by highlighting the potential for these materials to be realized in real materials and the broader implications for the study of topological phases in band insulators.This paper introduces the concept of "topological crystalline insulators," which are three-dimensional materials with metallic surface states characterized by quadratic band degeneracy on high-symmetry crystal surfaces. These materials are the counterpart of topological insulators in materials without spin-orbit coupling, where electron orbital degrees of freedom play a role similar to spin. The authors extend the topological classification of band structures to include crystal point group symmetries, specifically focusing on four-fold ($C_4$) and six-fold ($C_6$) rotational symmetries. They introduce a new $\mathbb{Z}_2$ topological invariant to characterize the band structures of these materials, which is crucial for understanding their topological stability and the existence of gapless surface states. The paper also discusses the electronic properties of these surface states and provides a tight-binding model to illustrate the formation of gapless surface states on the (001) surface. The authors conclude by highlighting the potential for these materials to be realized in real materials and the broader implications for the study of topological phases in band insulators.