Density functional theory (DFT) using the local density approximation or the generalized gradient approximation for the description of exchange and correlation of the electrons has been the workhorse of theoretical solid state physics since the last few decades. Although a lot of materials are described successfully using these methods, the number of cases steadily grows where standard DFT calculations are not sufficient to give accurate results. This concerns for instance ground state properties like lattice parameters of solids, in particular also excited state properties (spectroscopy), since DFT is a theory of the ground state. In this work improved exchange-correlation functionals for the electrons and many body perturbation theory methods within the full potential augmented plane wave method using the WIEN2k package are investigated and applied to selected materials and their properties, where standard DFT calculations are not accurate enough. In the first part of this work the so called F center in lithium fluoride is investigated. The F center is the simplest type of color center, which is created, when a single fluorine atom is removed from the host crystal. Different schemes for the DFT exchange and correlation are compared such as the functionals PBE, YS-PBE0 and TB-mBJ, but also the GW method. Since the removal of a single fluorine leaves an electron of a lithium strongly localized in the vacant fluorine site, strong excitonic (or electron-hole) effects are present. These effects are included by solving the Bethe-Salpeter equation for electron-hole pairs. Additionally the results have been closely compared to quantum chemistry calculations. Very good agreement is found between our calculations using TB-mBJ and GW (plus Bethe-Salpeter corrections), quantum chemistry calculations and experiment. In the second part the methods established for lithium fluoride have been applied to other alkali halides. The dependence of their absorption energy on the lattice parameter, or the Mollwo-Ivey relation which states that the absorption energy with respect to the lattice constant has an exponential decay, has been studied since the 1920s. Good agreement is found between our calculations and experiment. Previous investigations claimed that the Madelung potential is the main factor for the Mollwo-Ivey behavior. Our investigations prove that ion-size effects and exchange of the electrons play the major role. The last part is dedicated to the investigation of correlation energies obtained from the adiabatic connection fluctuation dissipation theorem. This method links the response function to the correlation energy and is in principle exact. We investigate the convergence of the correlation energy within the random phase approximation. Finally geometrical properties of selected materials are calculated and compared to former calculations and experiment. Although we find good agreement for materials, such as diamond, Ar and Kr, in many cases we have some differences to former calculations and experiment that are not negligible. The disagreements might be due to the possible neglect of core states in the calculation of the correlation energy and to incomplete basis sets for the excited states within the spheres around the atoms. Unfortunately we cannot exclude possible errors in our code.