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Topic of the thesis is a theoretical description of the ultracold atomicgases in one- and two-dimensional optical lattices in the presence of thedisorder leading to the Anderson localization. The disorder is created byinteraction of the main fraction of atoms with the second immobilized fractiondistributed randomly over the lattice.  In low-dimensional systems there is no transition from the Anderson localizedto the conducting phase, although in the presence of correlations a discreteset of extended states can exist. The first part of the thesis is devoted toproperties of such states. In the finite size lattices, the presence of thosestates results in the appearance of `windows of transport' -- energy ranges, inwhich the localization length is longer than the system size.The analyticalmethod of determining the extended states energies for correlations ofgeneralized $N$-mers type is presented, along with a proof that indeed thosestates are extended in the infinite system. Subsequently, the way ofexperimental creation of this type of correlations is proposed, as well as thetechnique of generation of the disorder in the tunneling amplitudes, whichsignificantly enhances tunability of the proposed energy filters.  The second part of the thesis describes the method which allows to simulate aspecific type of the disorder: random magnetic field. Systems of such a class,created in a two dimensional lattice using simultaneous fast periodicmodulation of the lattice height and interactions with immobilized species, mayallow in future to investigate the range of topics from the condensed matterphysics, for example fractional quantum Hall effect at half-filling. In thethesis, the most interesting features observed upon investigation of suchsystems are presented. Especially, the anomalously low localization length forcorrelated disorder is explained.

Anderson Localization in Low-Dimensional Optical Lattices