Thesac (symmetry-adapted cluster) andsac-ci (sac-configurational interactions) theories have been applied to the calculations of the potential curves of the ground and excited states of the CO molecule. The states studied are valence typeX1Σ+, (4)1Σ+,A2Π,I1Σ−,D1Δ,a3Π,a′3Σ+,d3Δ, ande3Σ−1, and of Rydberg typeB1Σ+,C1Σ+, andF1Σ+. For the description of theX1Σ+ and (4)1Σ+ states, we took advantage of the fact that thesac andsac-ci solutions satisfy orthogonality and Hamiltonian orthogonality to each other. Near the avoided crossing region of these states, however, thesac theory fails because of the multi-reference nature of the correlation. Our theoretical potential curves of the ground and various excited states are very similar to therkr (Rydberg-Klein-Rees) potential curves based on experimental data. The spectroscopic constants calculated also agree well with experimental values.