The book includes five Chapters and the sequence is arranged so as reader gets the basic understanding of the subject and get idea of recent research work done so far in the field of rare earth compounds. The work in this book is focused on the detailed study on the heavy rare earth metals and some compounds of rare earths like dysprosium monopnictides, and gadolinium compounds those have wide range of technological applications. Chapter one is devoted to the basic introduction of the rare earth metals and their compounds the relevant theory of electronic, optical and magneto-optical properties. In the second chapter a detail study of ground state properties and optical and magneto-optical properties of heavy rare earth elements have been given. The third chapter is devoted to the calculations of reflectivity and magneto-optical properties of Dy monopnictides (DyX, X = N, P, As, Sb, Bi) which are semi-metallic in nature. In the forth chapter a comparative study of electronic, optical and magneto-optical properties of GdFe2 and GdCo2 compounds is discussed in details. In the last fifth chapter summary and conclusions along with future prospects is given.