Intense research into contemporary movements of the Earth Crust started in the middle of the 20-th century. The purpose is to study the geodynamic processes in the upper layers of the Earth Crust using geodynamic methods mainly with the purpose of predicting earthquakes. The historical (presatellite) information about basic work on geodynamic research is briefly given. The work have been made using geodesic methods within special programs mainly within the system of the Main branch of geodesy and cartography of the USSR (GUGK of the USSR). But at the beginning as an example of such research made by other organizations the research with the Academy of Science of the USSR (AN USSR) made at Garm geodynamic polygon are briefly characterised.