This experimental research program is aimed at the study of atomic coherence and interference phenomena manifested by electromagnetically induced transparency (EIT) in cold atoms and the exploration of related applications in nonlinear optics and quantum optics. Because of the negligible Doppler broadening and the dense atomic density in a magneto-optical trap, cold atoms are well suited for the proposed studies, and quantitative comparison between experimental measurements and theoretical calculations can be obtained. Several research projects such as slow-light nonlinear wave mixing at low light intensities, which may lead to photon correlation and entanglement, EIT enhanced Kerr nonlinearity and cross phase modulation, group velocity matching for enhanced EIT nonlinearity, cavity meditated EIT, cavity enhanced EIT Kerr nonlinearity and cross phase modulations will be studied. The broader impact of the program involves student education, particularly of members of under-represented groups at the university.