  The theory of plasma physics offers a number of nontrivial examples of
partial differential equations, which can be successfully treated with symmetry
methods. We propose the Grad-Shafranov equation which may illustrate the
reciprocal advantage of this interaction between plasma physics and symmetry
techniques. A symmetry classification of the Grad-Shafranov equation with two
arbitrary functions $F(u)$ and $G(u)$ of the unknown variable $u=u(x,t)$ is
given. The optimal system of one-dimensional subalgebras is performed. This
latter provides a process for building new solutions for the equation.
