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Preface 1. Introduction 2. Historical survey 3. Instrumentation 4. Wave properties of electrons 5. The diffraction conditions 6. Geometrical features of the patterns 7. Kikuchi and resonance patterns 8. Real diffraction patterns 9. Electron scattering by atoms 10. Kinematic electron diffraction 11. Fourier components of the crystal potential 12. Dynamical theory: transfer matrix method 13. Dynamical theory: embedded R-matrix method 14. Dynamical theory: integral method 15. Structural analysis of crystal surfaces 16. Inelastic scattering in a crystal 17. Weakly disordered surfaces 18. Strongly disordered surfaces 19. RHEED intensity oscillations Appendices A. Fourier representations B. Green's function C. Kirchhoff's diffraction theory D. A simpler Eigenvalue problem E. Waller and Hartree equation F. Optimization of dynamical calculation G. Scattering factor References.