I. General introductionII. The method of the most probable distributionIII. Discussion of the Nernst theoremIV. Examples on the second section(a) Free mass-point (ideal monatomic gas) (b) Planck's oscillator (c) Fermi oscillatorV. FluctuationsVI. The method of mean valuesVII. The n-particle problemVIII. Evaluation of the formulae. Limiting casesThe entropy constantThe failure of the classical theory. Gibb's paradoxDigression: Annihilation of matter?Digression on the uncertainty relationGas-degeneration properWeak degenerationMedium degenerationStrong degeneration(a) Strong Fermi-Dirac degeneration(b) Strong Bose-Einstein degenerationIX. The problem of radiation Appendix