Abstract
This paper aims at discussing two issues that can have a significant impact on the foundations of the theory of gravitation: 1. The existence of relativity of the space-time geometry with respect to the properties of the reference frame used, which is a manifestation of the well-known fact of relativity of geometry of space and time with respect to properties of measuring instruments (Henri Poincare). 2. The existence of invariance of the equations of motion of test particles with respect to geodesic (projective) mappings of the metric tensor in any given coordinate system. Because of this, even in a fixed coordinate system, gravitation is described in general by a continuous set of physically equivalent metrics.
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