INTRODUCTIONIn experimental studies on catalytic asymmetric synthesis, considerable attention has been paid to the interaction between chiral catalysts and the reactants to achieve high enantioselectivity. However, very little attention has been paid to the interaction between the enantiomers of a chiral catalyst when this catalyst is not enantiomerically pure.Examples of catalytic asymmetric synthesis have been reported in which the enantiomeric purity of the product is much higher than that of the chiral catalyst. A positive nonlinear effect (NLE), that is, asymmetric amplifi cation, is synthetically useful because a chiral catalyst with high ee is not needed to prepare a chiral product with high ee (Scheme 12.1 ).In asymmetric autocatalysis, the chiral catalyst P * and the product P * have the same structure; that is, the chiral product P * acts as a chiral catalyst P * for its own multiplication. Asymmetric autocatalysis differs from conventional catalytic asymmetric syntheses where the chiral catalyst C * and the product P * have different structures (Scheme 12.2 ).Highly enantioselective asymmetric autocatalysis has recently been reported. In such reactions, a trace amount of chiral molecule automultiplies without the assistance of another chiral molecule. Moreover, asymmetric autocatalysis with an amplifi cation of Catalytic Asymmetric Synthesis, Third Edition, Edited by Iwao Ojima