  Density functional theory is a preferred microscopic method for calculation
of nuclear properties over the whole nuclear chart. Besides ground-state
properties, which are calculated by Hartree-Fock theory, nuclear excitations
can be described by means of Random Phase Approximation (RPA). The main
objective of the present work is to give Skyrme RPA formalism for spherically
symmetric nuclei, using the techniques of angular-momentum coupling. Various
auxiliary topics, such as Hartree-Fock theory, Coulomb integral, center-of-mass
corrections and pairing, are treated as well. RPA method is derived also for
axially deformed nuclei. The derived formulae are then implemented in the
computer code and utilized for calculation of some physical results. After
thorough investigation of the precision aspects of the calculation, the
following topics are treated as examples: toroidal nature of the low-energy
(pygmy) part of the E1 resonance, giant resonances of various multipolarities
in deformed nucleus Sm-154, and magnetic dipole (M1) transitions in deformed
Cr-50.
  Keywords: Random Phase Approximation, Skyrme functional, giant resonances in
nuclei, reduced matrix elements
  I thank Jiri Mares and F. Knapp for their comments, which were taken into
account in the first revision.
