R.J. Baxter is a leader in statistical mechanics. His first work was the exact solution of a one-dimensional Coulomb plasma. He has established new relations between distribution functions and made a considerable contribution to the Percus-Yevick theory of real gases by showing how it can give a phase transition. Baxter has received international recognition for the solution of models with particles on two-dimensional lattices. His eight-vertex model contains as special cases the square lattice Ising model, the dimer, ice, F and KDP models. Later the Ising model with interaction between three neighbouring spins on a triangular lattice was solved. The solutions show how the critical exponents sometimes depend on the details of the interactions between particles, in contrast to the commonly held hypothesis that critical exponents depend only on the dimensionality and symmetry of the model.