Albert Einstein (1879-1955) used a different line of thought to study the physical properties of gravitational fields before he established the general theory of relativity on the mathematical basis of Riemannian geometry. Based on this idea, we developed a new theory of gravity that describes the physical properties of gravitational fields on the basis of special relativity and eventually unifies the electromagnetic and gravitational fields. This paper is only the first part of this new gravitational theory, focusing on the construction of the foundation of the new theoretical system, with the following main contents:1.A new view of space-time is put forward, which holds that time, space and the mass of matter are determined by the gravitational field, and therefore controlling the gravitational field can control the space-time and the mass of matter to a certain extent.2. Recalculating and reinterpreting the classical verification experiments of general relativity (including the gravitational redshift of light frequencies, the gravitational deflection of light, the Mercury perihelion procession shift, etc.) in accordance with the new theory of gravity yielded identical calculations to those of general relativity.3.On the basis of the observed speed of motion of the centre of mass of the solar system with respect to the stationary reference system of the cosmic microwave background radiation (CMBR), it was calculated that a 1-year cycle variation should be included in the complex variation of the Earth's rotation rate. In this cycle, the change in the length of day (ΔLOD) of the Earth decreases by about 0.77376 ms to 0.85972 ms in August compared to February each year. We analyse that this calculation is consistent with the observation data released by IERS (International Earth Rotation Service).4.The new gravitational theory explains the dark energy in the Universe.5.We have revised De Broglie's matter wave formula, and the revised matter wave formula can explain why matter cannot be cooled to absolute zero, and this new matter wave formula can be used as the basis for unifying the electromagnetic field and the gravitational field. We believe that fluctuations in matter (matter waves) generate gravitational fields, and that regulating matter waves regulates the generation of gravitational fields.6. We have designed and built the world's first gravitational field generator since 2016 based on this new theory of gravity, and have successfully conducted a gravitational field generator (curvature engine) experiment in 2021, which is briefly described in this paper.