Membranes composed of amphiphilic molecules are highlyflexible surfaces that determine the architecture ofbiological systems and provide a basic structural elementfor complex fluids such as microemulsions. Recently, avariety of new experimental methods such as X-rayscattering, neutron scattering, and atomic force microscopyhave been used in order to study themolecular structure ofthese membranes. Their conformational behavior, on the otherhand, is studied by optical and electron microscopy, whichreveals that membranes in aqueous solution exhibit anamazing variety of different shapes. Several theoreticalconcepts are described suchas bending elasticity,curvature, and minimal surfaces in order to understand thispolymorphism. These concepts are also useful to describe thebehavior of membranes in complex fluids where they can buildup hexagonal, lamellar, triply-periodic, cubic, and spongephases. The contributions to this volume provide anup-to-date overview and describe thestate-of-the-art ofthis rapidly evolving field of research.