Atomic Structure Theory is a textbook for students with a background in quantum mechanics. The text is designed to give 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. Numerical methods for solving the Schrödinger and Dirac eigenvalue problems and the (Dirac)-Hartree-Fock equations are given as well. B-spline basis sets are used to carry out sums arising in higher-order many-body calculations. Illustrative problems are provided, together with solutions. FORTRAN programs implementing the numerical methods in the text are included.