In this book, the mathematical principles and working methods of single-particle reconstruction are described; a method designed to retrieve three-dimensional structural information from electron micrographs showing thousands of “copies” of biological molecules trapped in a thin layer of ice. This technique is uniquely suited to obtain three-dimensional images of molecular machines in different functional states, as it dispenses with the need for crystals. The book starts with an introduction of image formation in the electron microscope, which includes the definition of the contrast transfer function. Next, averaging techniques and tools for image alignment, multivariate data analysis, and classification are described. An introduction into the mathematical principles underlying reconstruction of an object from its projections is followed by detailed accounts on how projection angles are determined, and how reconstruction is done in practice. The book concludes with a chapter on interpretation of density maps reconstructed, including methods for segmentation as well as fitting and docking of atomic coordinates.