  A practical high-accuracy relativistic method of atomic structure
calculations for univalent atoms is presented. The method is rooted in the
coupled-cluster formalism and includes non-perturbative treatment of single and
double excitations from the core and single, double and triple excitations
involving valence electron. Triple excitations of core electrons are included
in the fourth-order of many-body perturbation theory. In addition,
contributions from the disconnected excitations are incorporated. Evaluation of
matrix elements includes all-order dressing of lines and vertices of the
diagrams. The resulting formalism for matrix elements is complete through the
fourth order and sums certain chains of diagrams to all orders. With the
developed method we compute removal energies, magnetic-dipole
hyperfine-structure constants A and electric-dipole amplitudes. We find that
the removal energies are reproduced within 0.01-0.03% and the hyperfine
constants of the 3s_1/2 and 3p_1/2 states with a better than 0.1% accuracy. The
computed dipole amplitudes for the principal 3s_1/2 - 3p_1/2;3/2 transitions
are in an agreement with 0.05%-accurate experimental data.
