The first link below is to the original paper on similarity solutions. The most complete discussion, which highlights the connections between quantum field theory and PDEs is in my book Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, 1992), chapter 10.

The second link is to a long and detailed paper on global asymptotic analysis, describing the RG approach to multiple scale analysis, boundary layer theory, WKB, matched asymptotic expansions, reductive perturbation theory and center manifold theory.

Other topics not covered in the lecture include: RG methods for travelling front problems, RG approaches to numerics for PDEs and stochastic differential equations. References to them can be found here (Physical Review access required).

http://publish.aps.org/abstract/prl/v64/p1361
http://publish.aps.org/abstract/pre/v54/p376