The present work is dedicated first to a systematic investigation of the initial growth stages of epitaxial BaTiO3 films growing on (001)-oriented Nb-doped SrTiO3 (SrTiO3:Nb) substrates, when deposited by pulsed laser deposition (PLD). Second, the obtained insight into the initial growth stages of BaTiO3 films was used to grow BaTiO3/SrTiO3 multilayers by PLD under well-controlled growth conditions. TiO2-terminated surfaces of (001)-oriented single crystal SrTiO3:Nb substrates have been prepared by a definite chemical and thermal treatment. Initial growth stages and the growth mechanism of epitaxial BaTiO3 films and BaTiO3/SrTiO3 multilayers on (001) SrTiO3 substrates are studied in terms of surface morphology, crystalline orientation, microstructure and interface morphology, using a combined application of atomic force microscopy (AFM), high-resolution transmission electron microscopy (HRTEM), and x-ray diffraction (XRD). For the first time a Stranski-Krastanov growth mechanism was found to govern the growth in a BaTiO3/SrTiO3 system. Under specific deposition conditions, the layer-by-layer growth was followed by an island growth at a nominal thickness of the BaTiO3 film of about 5 nm. Later on, these small grains coalesce into large grains at a nominal thickness of the BaTiO3 layer of about 75 nm followed by a columnar structure developed for thicker films. Epitaxial BaTiO3/SrTiO3 multilayers showed the Stranski-Krastanov growth mechanism of the BaTiO3 layers. Up to 6 nm in thickness, the BaTiO3 films showed no defects and sharp BaTiO3/SrTiO3 interfaces. In multilayers consisting of thick individual layers, an asymmetry of the morphology was observed between SrTiO3-on-BaTiO3 and BaTiO3-on--SrTiO3 interfaces. This feature is explained by a difference in the morphological stability of the two boundary surfaces. Dielectric measurements have been performed on Pt/BaTiO3/SrTiO3:Nb and Pt/BaTiO3/... /SrTiO3/BaTiO3/SrTiO3:Nb heterostructures with different thickness of the individual BaTiO3 and SrTiO3 layers. Thickness dependence of the dielectric constants of BaTiO3 films and BaTiO3/ /SrTiO3 multilayers exhibits a change in their linear slopes at a thickness of 75 nm. This behaviour is explained by the change observed in the morphology at a thickness of 75 nm, as well as by dead layers extended vertically along the column boundaries.