Cercignani provides a stimulating biography of a great scientist. Boltzmann's greatness is difficult to state, but the fact that the author is still actively engaged in research into some of the finer, as yet unresolved issues provoked by Boltzmann's work is a measure of just how far ahead of his time Boltzmann was. It is also tragic to read of Boltzmann's persecution by his contemporaries, the energeticists, who regarded atoms as a convenient hypothesis, but not as having a definite existence. Boltzmann felt that atoms were real and this motivated much of his research. How Boltzmann would have laughed if he could have seen present-day scanning tunnelling microscopy images, which resolve the atomic structure at surfaces! If only all scientists would learn from Boltzmann's life story that it is bad for science to persecute someone whose views you do not share but cannot disprove. One surprising fact I learned from this book was how research into thermodynamics and statistical mechanics led to the beginnings of quantum theory (such as Planck's distribution law, and Einstein's theory of specific heat). Lecture notes by Boltzmann also seem to have influenced Einstein's construction of special relativity. Cercignani's familiarity with Boltzmann's work at the research level will probably set this above other biographies of Boltzmann for a very long time to come.

WHen people ask me for a book to learn non-equilibrium statistical
mechanics the answer has to be: Cercignani's:the Boltzmann
equation; theory and apllications. That book was a real
mastepiece and many years later is still THE book in kinetic theory.

With this new book the first author 'stikes again' this time for
relativistic particle dynamics. In this complete and super
appealing work everything you need to know about relativistic
kinetic theory is included at affordable prize. The calculations
are detailed, the coverage justified and natural.

It should be (together with the first) in every mathematics library.

Written by some of the masters of the italian school of mathematical-physics, this book is a survey of rigorous results on the Boltzmann equation and various topics surrounding it. Trying to organize such an amount of material in a 350 pgs. book is an ambitious and breathtaking task. So the book is not an easy and systematic treatise, but a compilation of diverse results in the area, which is very needed, as they are scattered in a vast technical literature. Particularly welcome is a complete exposition of Landford's result on the validity of the Boltzmann equation, a (partial) realization of Boltzmann's dream and a real triumph of mathematical-physics. On the other hand, the chapter on hydrodynamic limits is extremely concise.

In any case, this book should be a standard reference in the field. Indicated to mathematical-physicists and mathematicians alike.