Sewell, G. L. Developments in normal and gravitational thermodynamics (24K, TeX) ABSTRACT. We review developments in three areas of thermodynamics, resulting from advances in statistical mechanics and relativity theory. These concern (a) the resolution of some basic questions, concerning the thermodynamic variables and the phase structure of normal matter, (b) thermodynamical instabilities in non-relativistic gravitational systems, and (c) Black Hole thermodynamics, as formulated in terms of strictly observable quantities, and thus not involving any BH entropy concept.