the broad theoretical concepts and group characteriza­ tion of Chapter Two to cover, in a somewhat more detailed manner, the derivation of the spin- Hamiltonian for this case. In Chapter Two, mention is made of the fact that for the 4f rare earth ions the spin­ orbit coupling energy is in general large compared to the crystal field influence of the surrounding ligand matrix. In such a case, the quantum number J is a good quantum number for the rare earth ion in question and the crystal field effects are taken into account within 1M, states. In this formulation, which is pursued in detail in this book, the effects of spin-orbit coupling have been taken care of at the very outset by the d~"ining of the 1M, states.