Bethe's dynamical theory of electron diffraction in crystals is developed using the approximation of nearly free electrons and Brillouin zones.The use of Brillouin zones in describing electron diffraction phenomena proves to be illuminating since the energy discontinuity at a zone boundary is a fundamental quantity determining the existence of a Bragg reflection. The perturbation of the energy levels at a corner of a Brillouin zone is briefly discussed and the manner in which forbidden reflections may arise at a corner pointed out. It is concluded that the kinematic theory is inadequate for interpreting electron images of crystalline films.An electrolytic method for preparing thin metal sections for electron microscopy and diffraction is introduced and its application to the structure of cold‐worked aluminum and an aluminum‐copper alloy demonstrated. It is concluded that cold‐worked aluminum initially consists of small, inhomogeneously strained and disoriented blocks about 200A in size. These blocks are not revealed by etching but would contribute to line broadening in the conventional diffraction experiments. By means of a reorientation of the blocks through a nucleation and growth process, larger disoriented domains about 1–3&mgr; in size found experimentally could be accounted for. It is suggested that such a nucleation and growth reorientation phenomenon is responsible for self‐recovery in cold‐worked metals.The formation of CuAl2precipitate particles is demonstrated with both electron micrographs and diffraction patterns. A fine lamellar structure found in the quenched Al‐4 percent Cu alloy is at present unexplained.