A small complement to Abdelmalek Abdessalam's answer: on the rigorous, non-perturbative side, there is also a recent exposition by Jonathan Dimock (<a href="http://arxiv.org/abs/1108.1335">"The Renormalization Group According to Balaban"</a>) using the $\phi^4$ scalar field theory in 3 dimensions in finite volume as a model for discussion. This paper is supposed to be the first of a two-part presentation. Tadeusz Balaban refined the method of block-spin renormalization group employed by Kupiainen and others for lattice field models in order to analyse "large field" regions, aiming at the treatment of the continuum limit of pure Yang-Mills models in finite volume and 4 dimensions. His long series of papers on the subject from the 80's remain essentially the state of the art towards the rigorous construction of realistic models in quantum field theory in 4 dimensions (see, for instance, the <a href="http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104178467">latest of the series</a>), together with the <a href="http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104253284">paper of Magnen, Rivasseau and Sénéor</a>, which was motivated by Balaban's work. Dimock's exposé doesn't touch the problem of large fields, which are saved for the sequel. Stay tuned...