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While the lanthanides (strictly defined as the 14 elements following lanthanum in the periodic table, but as normally used also include lanthanum itself) have several unique characteristics compared to other elements, their appearance in the history of the development of organometallic chemistry is rather recent. Since the f orbitals are filled gradually from lanthanum ([Xe]4f ) to lutetium ([Xe]4fl4), they are regarded as the f-block elements, which are discriminated from the d-block transition elements. This book was edited as the second volume of "Topics in Organometallic Chemistry", aiming at an overview of recent advances of chemistry and organic synthesis of lanthanides. Since scandium (Sc) and yttrium (Y) (which lie above the lanthanides and have similar characteristics) are also included, this book covers rare earth chemistry. Recently, especially in this decade, the chemistry and organic synthesis of lanthanides have developed rapidly as one of the most exciting areas.An international team of authors has been brought together in order to provide a timely and concise review of current research efforts such as lanthanide catalysis in small molecule organic synthesis especially focused on carbon-carbon bond-forming reactions, chemistry and organic synthesis using low-valent lanthanides such as diiodosamarium, asymmetric catalysis, lant- nide-catalyzed polymer synthesis, and polymer-supported lanthanide catalysts used in organic synthesis. Principles of organolanthanide chemistry are sum- rized in the first chapter. I am sincerely grateful to Drs. R. Anwander, E. C. D- dy, H. Gr6ger, Z. Hou, H. Kagan, G. Molander, J. L. Namy, M. Shibasaki, Y.