This book describes the recent evolution of rare earth elements and their mineralogy, both natural and synthetic analogues. Authors review and document rare earth element chemistry in the aqueous environment and the petrology of the rare earth element-bearing mineral Allanite. Synthetic rare earth minerals and their applications is a rapidly evolving discipline important to medicine, advanced digital technologies, and solid-state physics. Authors report on the synthesis of a macrocyclic gadolinium complex and also gadolinium complexes and their applications in medicine. Authors present compelling advances in gadolinium isotopes and oxides as substrates for induced excitation and luminescent material sciences.