Molecular dynamics simulations are used in order to study the self-assembly process and the physical properties of flexible membranes composed of amphiphilic molecules. On molecular scales; these membranes are observed to be rather mobile and to have rough surfaces arising from molecular protrusions; i.e.; from the relative displacements of individual molecules. On length scales that are only somewhat larger than the membrane thickness; on the other hand; the membranes are found to undergo smooth bending undulations. In this way; our study provides the first explicit connection between computer simulations with molecular resolution and elastic membrane models based on differential geometry.