Meshes are the most commonly used objects in computer graphics. They generalize polyhedra by using non-planar faces. Modeling 2-dimensional manifold meshes with a simple user interface is an important problem in computer aided geometric design. In this work we propose a conceptual framework for mesh modeling systems that guarantees topologically correct 2-dimensional manifolds. Our solution is based on graph rotation systems developed in topological graph theory. As an internal representation of meshes, we use Doubly Linked Face List (DLFL). We have also developed a visual representation of the topology that provides a powerful tool for developing a user in-terface to manipulate the topology of the mesh.