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We present an introduction to modern theories of interfacial fluctuations andthe associated interfacial parameters: surface tension and surface stiffness,as well as their interpretation within the capillary wave model. Transfermatrix spectrum properties due to fluctuation of an interface in along-cylinder geometry are reviewed. The roughening transition and propertiesof rigid interfaces below the roughening temperature in 3d lattice models aresurveyed with emphasis on differences in fluctuations and transfer matrixspectral properties of rigid vs. rough interfaces.Comment: 21 page

FLUCTUATING INTERFACES, SURFACE TENSION, AND CAPILLARY WAVES: AN INTRODUCTION