  We derive optimal a priori and a posteriori error estimates for Nitsche's
method applied to unilateral contact problems. Our analysis is based on the
interpretation of Nitsche's method as a stabilised finite element method for
the mixed Lagrange multiplier formulation of the contact problem wherein the
Lagrange multiplier has been eliminated elementwise. To simplify the
presentation, we focus on the scalar Signorini problem and outline only the
proofs of the main results since most of the auxiliary results can be traced to
our previous works on the numerical approximation of variational inequalities.
We end the paper by presenting results of our numerical computations which
corroborate the efficiency and reliability of the a posteriori estimators.
