I'm looking for an introductory text on the theory of the Boltzmann equation. I'd be particularly happy with a short, self-contained text, e.g. a tutorial / set of lecture notes, but longer references would also be welcome. I also suspect there may be more general textbooks on PDE which include a section about the Boltzmann equation - this would also be suitable for my purposes.
Thus far, I've been working from Villani's "A review of mathematical topics in collisional kinetic theory". Whilst thorough and well-written, it is quite densely filled with references to other works. In line with this, I'm seeking a more elementary, restricted reference to complement Villani's review.
If relevant, my ultimate plan is to work towards understanding the theorems of Ukai (short-range interactions) and Gressman-Strain (long-range interactions). I should emphasise, however, that my reason for seeking a reference is to build my introductory knowledge of the Boltzmann equation.
I like very much Mathematical Statistical Mechanics, which can be used for "introductory knowledge".