  This is a colloquium-style review lecture for physicists and non-physicists,
as part of the requirements for ``Habilitation'' at the university of Bern: At
a pressure of 220 atm. and a temperature of 374 Celsius there is a second-order
phase transition between water and steam. Understanding it requires the concept
of the renormalization group. Images from computer simulations of the lattice
gas model (included) are used to explain its basic ideas. It is briefly
reviewed how the renormalization group is used to compute critical coefficients
for the water-steam phase transition, in good agreement with experiment.
Applications in particle physics and string theory are mentioned. The appendix
contains a sample of the author's results on renormalization group flows in
theories with dynamical gravity and their relation to perturbative string
theory: gravity modifies critical coefficients and phase diagrams, in agreement
with numerical calculations, and leads to curious phenomena such as oscillating
flows and quantum mechanical flows.
