The f-sum rule is introduced and its applications to electronic and vibrational modes are discussed. A related integral over the intra-band part of sigma(omega) which is also valid for correlated electrons, becomes just the kinetic energy if the only hopping os between nearest-neighbor sites. A summary is given of additional sum-rule expressions for the optical conductivity and the dielectric function, including expressions for the first and second moment of the optical conductivity, and a relation between the Coulomb correlation energy and the energy loss function. It is shown from various examples, that the optical spectra of high Tc materials along the c-axis and in the ab-plane direction can be used to study the kinetic energy change due to the appearance of superconductivity. The results show, that the pairing mechanism is highly unconventional, and mostly associated with a lowering of kinetic energy parallel to the planes when pairs are formed. Keywords: Optical conductivity, spectral weight, sum rules, reflectivity, dielectric function, inelastic scattering, energy loss function, inelastic electron scattering, Josephson plasmon, multi-layers, interlayer tunneling, transverse optical plasmon, specific heat, pair-correlation, kinetic energy, correlation energy, internal energy.