Multiplets of Transition-Metal Ions in Crystals provides information pertinent to ligand field theory. This book discusses the fundamentals of quantum mechanics and the theory of atomic spectra. Comprised of 10 chapters, this book starts with an overview of the qualitative nature of the splitting of the energy level as well as the angular behavior of the wavefunctions. This text then examines the problem of obtaining the energy eigenvalues and eigenstates of the two-electron systems, in which two electrons are accommodated in the t2g and eg shells in a variety of ways. Other chapters discuss the ligand-field potential, which is invariant to any symmetry operation in the group to which symmetry of the system belongs. This book discusses as well the approximate method of expressing molecular orbitals (MO) by a suitable linear combination of atomic orbitals (AO). The final chapter discusses the MO in molecules and the self-consistent field theory of Hartree-Fock. This book is a valuable resource for research physicists, chemists, electronic engineers, and graduate students.