  The dissertation presents possibilities of applying noncommutative spacetimes
description, particularly kappa-deformed Minkowski spacetime and Drinfeld's
deformation theory, as a mathematical formalism for Doubly Special Relativity
theories (DSR), which are thought as phenomenological limit of quantum gravity
theory. Deformed relativistic symmetries are described within Hopf algebra
language. In the case of (quantum) kappa-Minkowski spacetime the symmetry group
is described by the (quantum) kappa-Poincare Hopf algebra. Deformed
relativistic symmetries were used to construct the DSR algebra, which unifies
noncommutative coordinates with generators of the symmetry algebra. It contains
the deformed Heisenberg-Weyl subalgebra. It was proved that DSR algebra can be
obtained by nonlinear change of generators from undeformed algebra. We show
that the possibility of applications in Planck scale physics is connected with
certain realizations of quantum spacetime, which in turn leads to deformed
dispersion relations.
