Our research made an important contribution towards understanding of several soft matter systems. The knowledge gained in the fundamental research has been in part also transferred to the rapidly growing electrooptic technologies. 75 papers have been published in international scientific journals and in books; 6 of them appeared in Physical Review Letters. The applied research resulted in 6 patents and patent applications. We would like to mention in particular the following achievements: - Confined nematic liquid crystals: The stable structures of a chiral nematic liquid crystal in cylindrical cavity were successfully modeled. In order to elucidate the liquid crystal structures in complex confinement and to simulate the NMR spectra taking into account the molecular diffusion, an addapted Monte Carlo method has been used. Using NMR, we detected the orientational nematic and positional smectic wetting of solid surfaces. A phenomenological theory was used to account for the effect of surface modulation, elastic constants and flexoelectricity on the deformations of nematic structures in the vicinity of solid surfaces. - Nematic and smectic defects: Brownian molecular dynamics on a semimicroscopic lattice was used to study the growth of nematic domains in different constraining geometries. Different scenaria, following the encounter of two defects with opposite sign, were identified. Depending on the scale of the confining geometry the structure may be either with defects or defectless. Using a phenomenological theory, we showed that the hydrodynamic back-flow induces differences in the velocities of defects of opposite sign. Further the origin and distribution of edge dislocations due to the memory effects in confined smectic A liquid crystals was analized. - Structural forces, ordering, and fluctuations: The AFM results obtained for a nematic liquid crystal in the isotropic phase were explained on the basis of nematic capillary forces. The Casimir interaction was discussed in view of the fluctuations within a layer with complete orientational wetting. We showed that also Monte Carlo simulations give a reliable insight into the fluctuations in the confined nematic phase. - Liposomes: The problem of unusual nuclear spin relaxation in lipid membranes has been solved. We showed that it arises from the fluctuations in the shape of spherical vesicles that can be described by a discrete set of fluctuation modes. The spin relaxation measurements reveal thus the viscoelastic properties of biological membranes. They are important in the optimization of vesicles when applied for the transport of genes and other pharmacological substances. - Colloid and polymer dispersions: A polymer network dispersed in the liquid crystalline cell can improve considerably its electro-optical properties. Monte Carlo simulations were used to study the influence of the polymer network morphology on the swiching of the cell between the on- and off-state. A polymer network in the periodic chevron structure of a ferroelectric cell, improves its mechanic stability as well as its electrooptic properties. The ferroelectric liquid crystals are strongly influenced also by the presence of colloidal particles. A small number of them is sufficient to cause the diapearence of the Goldstone mode of orientational fluctuations. - Molecular motors: A model of the binding of dimers and oligomers on biological polymers with periodic binding sites was developed. It allowed for an interpretation of equilibrium and dynamic phenomena studied by decoration experiments. Further the instabilities in the transient response of muscles and the adaptation processes in auditory receptors were modelled - Liquid crystal optical switches: An optimization of the optical properties of the LC switches was achieved using modelling the structural and optical parameters.