Smooth-Automorphic Forms and Smooth-Automorphic Representations : World Scientific Publishing : 9789811246166 : 9811246165 : 22 Jun 2023 : This book provides a thorough introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F. Our approach to automorphic representations is, however, different to what one usually finds in the literature: We do not restrict ourselves to considering ""K-finite"" automorphic forms, but allow a richer class of only smooth functions. In this way, we regain a perfect symmetry between the archimedean and the non-archimedean places of our number field F, making our bigger space of ""smooth automorphic forms"" a proper, continuous representation of the full group of adelic points of G. This book is a unique source, where a theory of ""smooth automorphic representations"" is developed and presented in great detail.