This book describes the generalized Sturmian method, which offers a fresh approach to the calculation of atomic spectra. Generalized Sturmians are isoenergetic solutions to an approximate many-electron Schrodinger equation with a weighted potential. The weighting factors are chosen in such a way as to make all of the solutions correspond to a given energy. The advantage of such an isoenergetic basis set is that every basis function has the correct asymptotic behavior needed for efficient synthesis of the wave function. The book also discusses methods for automatic generation of symmetry-adapted basis sets. Calculations using the generalized Sturmian method are presented and compared with experimental results from the NIST database. The relationship of Sturmians to harmonic polynomials and hyperspherical harmonics is also described. Methods for treating angular functions and angular integrals by means of harmonic projection are discussed, and these methods are shown to be especially useful for relativistic calculations. A final chapter discusses application of the generalized Sturmian method to the calculation of molecular spectra.