  The incompatibility between the treatment of time in the classical and in the
quantum theory results in the so-called problem of time in canonical quantum
gravity. For this reason, attempts have been made to devise algorithms of
quantization which accomodate the covariance of the classical theory from the
outset. One of the most prominent of these attempts is based on the notion of
continuous histories (Isham and Linden) in the context of the consistent
histories approach to quantum theory (Griffiths, Omnes, Gell-Mann and Hartle).
By the term continuous histories it is implied that the canonical fields and
the symplectic structure of the theory depend on time as well as space. The aim
of this thesis (in the form it was submitted to the University of London,
February 2000) is to show that, even at the purely classical level, a history
approach has several advantages (compared to its equal-time counterpart) when
it comes to discussing spacetime issues. This is illustrated here by reframing
and generalizing the derivation of geometrodynamics from first principles
(Hojman, Kuchar, Teitelboim) in the language of the history phase space.
