  The purpose of this work is to review, clarify, and critically analyse modern
mathematical cosmology. The emphasis is upon mathematical objects and
structures, rather than numerical computations. This paper concentrates on
general relativistic cosmology. The opening section reviews and clarifies the
Friedmann-Robertson-Walker models of general relativistic cosmology, while
Section 2 deals with the spatially homogeneous models. Particular attention is
paid in these opening sections to the topological and geometrical aspects of
cosmological models. Section 3 explains how the mathematical formalism can be
linked with astronomical observation. In particular, the informal,
observational notion of the celestial sphere is given a rigorous mathematical
implementation. Part II of this work will concentrate on inflationary cosmology
and quantum cosmology.

General Relativity and Quantum Cosmology