In this paper, the geometric property and structure of the Hamilton-Jacobi equation arising from nonlinear control theory are investigated using symplectic geometry. The generating function of symplectic transforms plays an important role in revealing the structure of the Hamilton Jacobi equation. It is seen that many fundamental properties of the Riccati equation can be generalized in the Hamilton-Jacobi equation, and, therefore, the theory of the Hamilton-Jacobi equation naturally contains that of the Riccati equation.