We describe the four most famous versions of the classical canonical formalism in the Einstein theory of gravity: the Arnovitt-Deser-Misner formalism, the Faddeev-Popov formalism, the frame formalism in the usual form, and the frame formalism in the form best suited for constructing the loop theory of gravity, which is now being developed. We present the canonical transformations relating these formalisms. © 2006 Springer Science+Business Media, Inc.