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The mesh generation process for two-dimensional problems is discussed. A mesh generator based on expert system methods is presented. For every corner of a closed polygon the corner-angle conditions are analyzed and different types of mesh primitives are generated. In every step of the mesh generation the conflict with the existing mesh is recognized, and an optimal action will be chosen. Thus, any area surrounded by a polygon, even those with a very sophisticated contour, can be successfully covered with a basis mesh. This mesh is improved by side-swapping and node-shifting algorithms, both optimizing the shape of the elements and the location of the nodes. Problem-oriented adaptive mesh refinement algorithms provide further optimization according to suitable criteria.