We give a series of three lectures to present elements of
a rigorous renormalisation group method and its application, from recent joint
work with Roland Bauerschmidt and David Brydges. The applications are to
two interesting models of critical phenomena in dimension four:
the weakly self-avoiding walk and the $n$-component $|\varphi|^4$
spin model for all $n \ge 1$. The results include statements concerning
scaling limits and critical exponents. For example, the susceptibility
has a logarithmic correction to mean field scaling, with exponent
$\frac{n+2}{n+8}$ for the logarithm in the $|\varphi|^4$ model, and
with exponent $\frac{1}{4}$ for the weakly self-avoiding walk.
The lectures will present the general setting for the work, present
the principal results, and discuss aspects of their proof.