This book provides hands-on experience with atomic structure calculations. Material covered includes angular momentum methods, the central field Schrödinger and Dirac equations, Hartree-Fock and Dirac-Hartree-Fock equations, multiplet structure, hyperfine structure, the isotope shift, dipole and multipole transitions, basic many-body perturbation theory, configuration interaction, and correlation corrections to matrix elements. The book also contains numerical methods for solving the Schrödinger and Dirac eigenvalue problems and the (Dirac)-Hartree-Fock equations. B-spline basis sets are used to carry out sums arising in higher-order many-body calculations. In addition, Atomic Structure Theory includes illustrative problems, together with solutions, as well as FORTRAN programs implementing the numerical methods in the text.