Membranes composed of amphiphilic molecules are highly

flexible surfaces that determine the architecture of

biological systems and provide a basic structural element

for complex fluids such as microemulsions. Recently, a

variety of new experimental methods such as X-ray

scattering, neutron scattering, and atomic force microscopy

have been used in order to study themolecular structure of

these membranes. Their conformational behavior, on the other

hand, is studied by optical and electron microscopy, which

reveals that membranes in aqueous solution exhibit an

amazing variety of different shapes. Several theoretical

concepts are described suchas bending elasticity,

curvature, and minimal surfaces in order to understand this

polymorphism. These concepts are also useful to describe the

behavior of membranes in complex fluids where they can build

up hexagonal, lamellar, triply-periodic, cubic, and sponge

phases. The contributions to this volume provide an

uptodate overview and describe thestateoftheart of

this rapidly evolving field of research.