This book systematically develops the theory of continuous representations onp-adic Banach spaces. Its purpose is to lay the foundations of the representation theory of reductivep-adic groups onp-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series. Written to be accessible to graduate students, the book gives a comprehensive introduction to the necessary tools, including Iwasawa algebras,p-adic measures and distributions,p-adic functional analysis, reductive groups, and smooth and algebraic...