"We propose to develop and apply novel methods of nonlinear spectroscopy to investigate the significance and consequences of coherent effects for a variety of photophysical and photochemical molecular processes. We will use coherent two-dimensional (2D) spectroscopy as an ideal tool to study electronic coherences.Quantum mechanics as described by the Schrödinger equation is fully coherent: The phase of a wavefunction evolves deterministically in the time-dependent case. However, observations are restricted to reduced “systems” coupled to an “environment.” The resulting transition from coherent to incoherent behavior on an ultrafast timescale has many yet unexplored consequences, e.g. for transport in photosynthesis, photovoltaics or other molecular “nanomaterials.”In contrast to conventional 2D spectroscopy, we will not measure the coherently emitted field within a four-wave mixing process but rather implement a range of incoherent observables (ion mass spectra, fluorescence, and photoelectrons). Yet we can still extract all the desired information using “phase cycling” with collinear pulse sequences from a femtosecond pulse shaper. This opens up a new range of interdisciplinary experiments and will allow for the first time a direct nonlinear-spectroscopic comparison of molecular systems in all states of matter. Specifically, we will realize 2D spectroscopy in molecular beams, liquids, low-temperature solids, and on surfaces including heterogeneous and nanostructured samples. Tuning the external couplings will help elucidating the role of the environment in electronic (de)coherence phenomena.Furthermore, we will combine 2D spectroscopy with subdiffraction spatial resolution using photoemission electron microscopy (PEEM). This enables us to map transport in molecular aggregates and other heterogeneous nanosystems in time and space on a nanometer length scale. Thus we access the intersection between the domains of electronics and nanophotonics."