This book is a collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. It presents a comprehensive overview of developments in representation theory of algebraic groups and quantum groups. Particularly noteworthy are papers containing remarkable results concerning Lusztig's conjecture on cells in affine Weyl groups. The following topics were discussed: cells in affine Weyl groups, tilting modules, tensor categories attached to cells in affine Weyl groups, representations of algebraic groups in positive characteristic, representations of Hecke algebras, Ariki-Koike and cyclotomic $q$-Schur algebras, cellular algebras and diagram algebras, Gelfand-Graev representations of finite reductive groups, Green functions associated to complex reflection groups, induction theorem for Springer representations, representations of Lie algebras in positive characteristic, representations of quantum affine algebras, extremal weight modules, crystal bases, tropical Robinson-Schensted-Knuth correspondence and more. The material is suitable for graduate students and research mathematicians interested in representation theory of algebraic groups, Hecke algebras, quantum groups, and combinatorial theory. Information for our distributors: Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. All commercial channel discounts apply.