The water wave problem is mathematically formulated as a free boundary problem for an irrotational flow of an inviscid and incompressible fluid under the gravitational field. It is well-known that the water wave problem has a variational structure. In fact, J. C. Luke (1967) gave a Lagrangian in terms of the velocity potential and the surface variation. M. Isobe (1994) and T. Kakinuma (2000) derived model equations for water waves and the model equations are the Euler-Lagrange equations to an approximated Lagrangian, which is obtained by approximating the velocity potential in Luke's Lagrangian. In this course, I introduce one of the model equations and explain the structure of the model and the solvability of the initial value problem.