Five contributions to the 3rd ESO-VLT Workshop ``Galaxy Scaling   Relations''
  In the first contribution the basic problems posed by the existence of the Fundamental Plane (FP), and its relations with the Virial Theorem are discussed. Various possibilities are presented that can produce the observed uniform departure from homology and/or from a constant stellar mass-to-light ratio. The role of orbital anisotropy and its relation with the FP thickness are also discussed. In the second contribution the observational evidence for the existence of a FP for galaxy clusters, analogous to that of ellipticals, is presented and discussed. In the third contribution the dynamical properties of $R^{1/m}$ spherical galaxies with variable orbital anisotropy are discussed. The stability of the models against radial--orbit instability is studied, and the consequences on the FP tilt and thickness are discussed. An innovative tool for the construction of Evolutionary Synthesis models of Stellar Populations is described in the fourth contribution. As an illustrative example, the evolution of the stellar mass-to-light ratios has been computed and the implications on the FP of elliptical galaxies are briefly discussed. Finally, in the fifth contribution, with the aid of the first large sample of X-ray emitting early-type galaxies with known kinematics, the effect of rotation on the X-ray emission, particularly with regard to the X-ray underluminosity of flat systems is discussed. The role of structural parameters as the ellipticity, the isophotal shape parameter $a_4/a$, and the inner slope of the surface brightness profile recently measured by HST are also investigated. 
A. Cappi, L. Ciotti, B. Lanzoni, C. Maraston, S. Maurogordato, S.   Pellegrini