  We present an introduction to modern theories of interfacial fluctuations and
the associated interfacial parameters: surface tension and surface stiffness,
as well as their interpretation within the capillary wave model. Transfer
matrix spectrum properties due to fluctuation of an interface in a
long-cylinder geometry are reviewed. The roughening transition and properties
of rigid interfaces below the roughening temperature in 3d lattice models are
surveyed with emphasis on differences in fluctuations and transfer matrix
spectral properties of rigid vs. rough interfaces.
