A group theoretical framework is proposed for a detailed characterization of the shapes of electronic charge distributions of general, asymmetric molecules. The proposed shape groups are the homology and cohomology groups of charge density contour surfaces. These shape groups depend on two real parameters, the charge density value a for the contour and a curvature parameter b. The two-parameter family of various homology groups and cohomology groups of charge density contour surfaces is independent of the symmetry properties of the molecules and gives a concise description of the dominant shape characteristics. For any fixed parameter value b these groups may change only at specific charge density values, characteristic to the given molecule. On the other hand, for a fixed-charge density contour the group changes induced by a change in the curvature parameter b provide a description of the fine details of the shape of the electron density. The changes in the structure of these groups follow strict algebraic relations, that provide a quantitative measure for shape-similarity between various molecules. The two-parameter shape group method is an extension of an earlier method proposed for biochemical applications.