The Nobel Prize in Physics 2011 was awarded to the puzzling discovery that the Universe is not only expanding, but doing so with ever increasing speed, whereas in the standard picture of cosmology it was expected to slow down. This acceleration could either be due to a new exotic matter component called dark energy which is repellent and would form the major ingredient of the cosmos. Alternatively, the laws of gravity as predicted by Einstein's general relativity may not be quite correct on cosmological scales and need to be modified. One of the best ways to pin down the properties of dark energy and test general relativity on cosmological scales is to study the large-scale distribution of matter in the Universe and its evolution, together with its gravitational interactions. In a novel approach to probe this distribution, I am going to simultaneously analyse the positions, the velocities, and the shapes of millions of distant galaxies. The clustering of galaxies in space provides a picture of the underlying matter distribution since galaxies trace the matter density. However, the picture is biased because galaxies preferentially reside in high-density regions, and this galaxy bias limits the cosmological information that can be extracted from clustering. Using galaxy velocity measurements, one can infer the coherent motions of galaxies due to the large-scale gravitational forces via so-called redshift-space distortions, causing apparent overdensities of galaxies when these are attracted by a large mass. This effect needs to be disentangled from the actual clustering of galaxies, which is again hindered by galaxy bias, so that the power of redshift-space distortions alone to constrain cosmological parameters is limited as well. General relativity predicts that large masses can deflect light rays similar to a magnifying glass - therefore the term gravitational lensing was coined for this effect. The images of distant galaxies are distorted by the gravitational lensing of the large-scale structure of the Universe between these galaxies and Earth. These 'cosmic shear' distortions directly map the intervening matter distribution, without any dependence on galaxy bias. In addition, cosmic shear also probes the geometry of the cosmos as it depends on the distances between the light sources, the lenses, and the observer. This potentially very powerful cosmological probe is plagued by intrinsic alignments of galaxy shapes which mimic the distortions characteristic of cosmic shear and hence limit the accuracy of cosmological measurements. The key to overcome the limitations of the three probes is to analyse them jointly and also include their cross-correlations into the analysis. This will lift degeneracies between parameters as for instance caused by the galaxy bias, and calibrate systematic effects such as the intrinsic alignment contamination of cosmic shear. With this technique I will obtain significantly better constraints on dark energy and the laws of gravity than from any individual probe, and the results will additionally be much less susceptible to systematic errors. This approach requires an imaging survey with excellent image quality to measure the shapes of faint and small galaxy images which overlaps with a redshift survey that allows for the accurate measurement of galaxy distances which are needed to measure clustering and redshift-space distortions. The research team that I am going to lead has access to a unique pair of such surveys. The quality and size of the joint data set is so good that I can target different types of galaxies at the same time and thus apply even more advanced techniques to eliminate systematic effects from the measurements. The joint scientific analysis will therefore yield unprecedented precision and accuracy on the properties of dark energy and the nature of gravity.