The rare earth elements form a fascinating group, resembling each other very closely in both physical and chemical properties. The close similarity of the behaviour of the elements led to difficulties in isolation of the elements in a state of high purity. Now that the separation and purification of these elements have been achieved, the chemistry and the industrial applications of the rare earth elements are drawing the attention of many scientists in the world, especially countries which possess vast reserves of rare earth minerals. Some of the applications of mixed rare earths are as metallurgical additives for ferrous and non-ferrous metals, fluid cracking catalysts, lighter flints, polishing compounds in glasses, carbon arc cores for lighting and hydrogen absorbing alloys for rechargeable batteries.Some of the salient applications of high-purity rare earth elements are cathode ray tubes, automotive catalytic converters, permanent magnets in computer technology and sound systems, lasers, phosphors, electric motors, optical fibres, and possible future applications such as in coloured pigments for plastics and paints, new catalysts, refrigeration systems and solid oxide fuel cells. In order to use rare earths successfully in various applications, a good understanding of the chemistry of these elements is of paramount importance. Nearly three to four decades have passed since titles such as "The Rare Earths" edited by F.H. Spedding and A.H. Daane, "The chemistry of the Rare Earth Elements" by N.E. Topp and "Complexes of the Rare Earths" by S.P. Sinha were published. There have been many international conferences and symposia on rare earths, as well as the series of volumes entitled "Handbook of Physics and Chemistry of Rare Earths" edited by K.A. Gschneidner and L. Eyring.Thus, there is a need for a new title covering modern aspects of rare earth complexes along with the applications. The present title consists of twelve chapters. The first chapter is an introduction covering definition, classification, properties, world reserves, methods of processing from ores, methods of separation both classical and modern, and analytical chemistry of rare earths, including classical and modern methods. The second chapter deals with quantum chemical considerations, s, p, d and f orbitals, electronic configurations, Pauli's principle, spin-orbit coupling and levels, energy level diagrams, Hund's rules, Racah parameters, oxidation states, HSAB principle, coordination number, lanthanide contraction, interconfiguration fluctuations.This is followed by a chapter dealing with methods of determination of stability constants, stability constants of complexes, thermodynamic consideration, double-double effect, inclined w plot, applications of stability constant data. The fourth chapter deals with complexes of rare earth elements with a variety of complexing agents, such as monocarboxylic acids, dicarboxylic acids, polycarboxylic acids like citric, nitrilotriacetic, ethylenediamine tetraacetic; beta diketones, ligands with nitrogen donors, macrocyclic ligands, ligands with sulphur donors, phosphines, cyanate, thiocyanate, selenocyanate, perchlorate, decaborates, acyclic and macrocyclic Schiff's bases, carboranes, selenides and tellurides.Structural chemistry of lanthanide complexes dealing with low coordination numbers, 6-, -7 and -8 coordination, dodecahedra, square antiprisms, hexagonal bipyramids, cubes and other structures, 9-coordination, high coordination numbers and organometallic structures is discussed in the fifth chapter. Organometallic complexes such as tris, bis and monocylopentadienyl complexes, cyclooctatetraenyl complexes, cyclopentadienyl-cyclooctatetraenyl complexes, indenyl complexes, fluorenyl complexes, complexes with other aromatic-ligands, callixerene complexes, NMR spectroscopy of organometallic complexes, vibrational spectra, and catalytic applications form the theme of the sixth chapter. Kinetics and mechanisms complex formation involving rate expressions, rate laws, dissociative and associative pathways, techniques used in probing reaction mechanisms, crystal field effects are discussed in the following chapter.Crystal field theory, intensities of 4f-4f transitions, Judd-Ofelt theory of electric-dipole transitions, covalency model of hypersensitivity, dynamic coupling mechanism, solution spectra, spectral data for complexes, solvent effects, fluorescence and photochemistry of lanthanide complexes are dealt with in spectroscopy of lanthanide complexes. Photoelectron spectroscopy of rare earths involving typical spectra, core levels, splitting due to exchange, spin-orbit coupling, binding energies, states arising due to ionization of fn configuration, interconfiguration fluctuation and surface oxidation phenomena are discussed in the next chapter. The following chapter deals with the important topic of lanthanide NMR shift reagents and their applications in elucidating structures. The penultimate topic deals with ecological, physiological and environmental aspects along with some interesting biological applications.In the final chapter, applications such as in metallurgy of steels, corrosion inhibition, catalysis, paints, cinema arc carbon and search light electrodes, polishing powders in optics, permanent magnets, ceramic superconductors, lasers, garnet films for magnetic bubble memory applications, nuclear applications, x-ray phosphors for medical radiology, fiber optics, photonics, electronics, magnetic resonance imaging (MRI) high-tech applications and fuel cells are elucidated. The authors studied in schools headed by pioneers in rare earth chemistry, have a combined experience of one hundred and fifty years in inorganic chemistry, rare earth complex chemistry, nuclear and radiochemistry of rare earths and supramolecular chemistry. The present monograph is a product of this rich experience.