Electron microscopic analysis can be used to determine the three-dimen
sional structures of macromolecules at resolutions ranging between 3 a
nd 30 angstrom. It differs from nuclear magnetic resonance spectroscop
y or x-ray crystallography in that it allows an object's Coulomb poten
tial functions to be determined directly from images and can be used t
o study relatively complex macromolecular assemblies in a crystalline
or noncrystalline state. Electron imaging already has provided valuabl
e structural information about various biological systems, including m
embrane proteins, protein-nucleic acid complexes, contractile and moti
le protein assemblies, viruses, and transport complexes for ions or ma
cromolecules. This article, organized as a series of lectures, present
s the biophysical principles of three-dimensional analysis of objects
possessing different symmetries.