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 up-to-date overview and describe thestate-of-the-art of this rapidly evolving field of research.

Biomembranes consist of molecular bilayers with many lipid and protein components. The fluidity of these bilayers allows them to respond to different environmental cues by changing their local molecular composition as well as their shape and topology. On the nanometer scale, this multi-responsive behavior can be studied by molecular dynamics simulations, which provide both snapshots and movies of the bilayer conformations. The general conceptual framework for these simulations is provided by the theory of curvature elasticity. The latter theory also explains the behavior of giant vesicles as observed by optical microscopy on the micrometer scale. The present volume describes new insights as obtained from recent developments in analytical theory, computer simulations, and experimental approaches. The seven chapters of the volume are arranged in a bottom-up manner from smaller to larger scales. These chapters address the refined molecular dynamics and multiscale modeling of biomembranes, their morphological complexity and adhesion, the engulfment and endocytosis of nanoparticles, the fusion of giant unilamellar vesicles, as well as recent advances in microfluidic technology applied to model membranes.