This volume is an outgrowth of the activities of the RIMS Research Project, which presented symposia offering both individual lectures on specialized topics and expository courses on current research. The subjects therein reflect very active areas in the representation theory of Lie groups. Also included are various topical interactions with geometry of homogeneous spaces, automorphic forms, quantum groups, special functions, discrete groups, differential equations, etc. Comprising results from some of today's most active areas of research, this volume will serve as an excellent up-to-date guide to the representation theory of Lie groups.