RESEARCH DESCRIPTION Our group has been developing the field of coherent multidimensional spectroscopy (CMDS), the optical analogue of multidimensional NMR methods. Our approach is unique in using a mixed frequency/time domain approach to CMDS. Our laser system creates multiple independently tunable sub-femtosecond excitation beams to excite a quantum mechanical superposition state involving multiple electronic and/or vibrational states of molecules and materials. The superposition state reemits multiple beams that are created by each pair of states within the superposition. Tuning the excitation frequencies provides multidimensional spectra with cross-peaks between quantum states that are coupled by intra- or inter-molecular interactions so CMDS is selective for interactions. Changing the time delays between excitation pulses provides the complete dynamics of the coherences and populations present in the superposition state. Frequency domain methods have the advantage that they uniquely define the quantum states involved in the superposition state, they can access zero and multiple quantum coherences, and their independently tunable excitation frequencies provides complete coverage over all quantum states of interest. We have applied these methods to measuring the electronic and vibrational states of molecules and the properties of materials. This work has provided the nonlinear methods of MENS, MEPS, SIVE, DOVE, and TRIVE four wave mixing spectroscopies. It has also led to the discovery of frequency domain quantum beating, coherence transfer, coherence transfer spectroscopy, and multiple quantum coherence spectroscopy. These nonlinear methods represent a new family of optical spectroscopies that will bring the selectivity of NMR methods to traditional optical spectroscopies. Our group's mission is to both continue developing this exciting new family of spectroscopies and applying the methods to materials science, chemical measurement, molecular spectroscopy, protein-protein, protein-DNA, DNA-DNA interactions, and coherent control of electron transfer dynamics. We expect coherent multidimensional nonlinear methods will take their place beside multidimensional NMR as one of our most powerful structural tools for studying chemical and biochemical systems.