The forward and direct inversion of complex gravity and magnetic field of regular 2D-bodies under the condition of undulate topography consists of four successive papers. The forward problem of complex gravity and magnetic fields is expounded in the first and the second paper. Mainly using Russian scholars' method, the author deduced strictly and simply the complex gravity and magnetic field expressions of regular 2D-bodies and their combination bodies in complex field. Compared with the gravity and magnetic field expressions of these bodies in rectangular coordinates system, these expressions of complex fields have very simple forms. In the third and the fourth paper, the direct inversion problem of complex gravity and magnetic fields is expounded, which makes up the core of the serial papers. In these two papers, according to the complex gravity and magnetic field expressions of regular 2D-bodies and their combination bodies, the author first established linear simultaneous equations for solving middle variables in the complex coordinates system by use of his creative method of linearization, then established the high order complex equation by use of middle variables to be solved out. As for the linear simultaneous equations and the high-order complex equation, the author solved successfully the direct inversion problem of complex gravity and magnetic fields of almost all regular 2D-bodies under the condition of undulate topography (or under the condition that the observation line lies in the arbitrary direction of 2D-anomaly sources or is even closed).