The objective of this work is twofold. First, we explore
the performance of the density functional theory (DFT)
when it is applied to solids with strong electronic correlations, such
as transition metal compounds. Along this direction, particular effort is put
into the refinement and development of parameterization techniques
for deriving effective models on a basis of DFT calculations.
Second, within the framework of the DFT, we address
a number of questions related to the physics of Mott insulators,
such as magnetic frustration and electron-phonon coupling (Cs2CuCl4 and Cs2CuBr4), high-temperature  superconductivity (BSCCO) and doping of Mott insulators (TiOCl).
In the frustrated antiferromagnets Cs2CuCl4 and Cs2CuBr4,
we investigate the interplay between strong electronic
correlations and magnetism on one hand and electron-lattice coupling
on the other as well as the effect of this interplay on the microscopic model parameters.
Another object of our investigations
is the oxygen-doped cuprate superconductor BSCCO,
where nano-scale electronic inhomogeneities have been
observed in scanning tunneling spectroscopy experiments.
By means of DFT and many-body calculations, we analyze the connection
between the structural and electronic inhomogeneities and the superconducting
properties of BSCCO.
We use the DFT and molecular dynamic simulations
to explain the microscopic origin of the persisting under doping
Mott insulating state in the layered compound TiOCl.