The article presents the fundamentals of the thermohydrogravidynamic theory of the global seismotectonic, volcanic, climatic and magnetic activity of the Earth based on the author’s generalized differential formulation of the first law of thermodynamics extending the classical Gibbs’ formulation by taking into account the infinitesimal increment of the macroscopic kinetic energy , the infinitesimal increment of the gravitational potential energy , the generalized expression for the infinitesimal work done by the non-potential stress forces acting on the boundary surface of the continuum region , the infinitesimal increment of energy due to the cosmic and terrestrial non-stationary energy gravitational influence on the continuum region , the differential change of the electromagnetic energy inside the continuum region , the energy flux of the electromagnetic energy radiated from the individual region across the boundary surface of the continuum region , the differential heating due to the differential work of electrodynamic forces (resulted to the Joule heating owing to the electrical currents inside the continuum region ). Based on the established fundamental global seismotectonic, volcanic, climatic and magnetic time periodicities and (determined by the combined predominant non-stationary energy gravitational influences on the Earth of the system Sun-Moon, the Venus, the Mars, the Jupiter and the Sun owing to the gravitational interactions of the Sun with the Jupiter and the Saturn), the author presents the evidence of the cosmic energy gravitational genesis of the forthcoming intensification of the global seismotectonic, volcanic, climatic and magnetic activity of the Earth in the 21st century AD related causally with the revealed (by Kleiven et al. in 2008 AD) outstanding climate anomaly during (6372÷6192) BC in the North Atlantic.