Very accurate electron structure factors measured by a significantly improved transmission electron diffraction technique for polycrystalline samples were used in a high-resolution quantitative study of the electrostatic potentials in LiF, NaF, and MgO crystals. The spatial electrostatic potential distribution was obtained using an analytical structural kappa -model adapted for electron diffraction. A topological analysis of the electrostatic potential, defining the features of the electrostatic field and the Coulomb force field in a crystal was developed. In addition to the topological analysis of the electron density, this approach provides a more complete description of the atomic interactions. The application of this approach to the characterization of bonding in a crystal has been demonstrated. The suitability of electron diffraction for determination of the core-electron binding energy is discussed.