Within the conception of movement of numerous coupled inflexible our bodies a few fastened aspect you will distinguish 3 simple ramifications. 1. the 1st, the so-called classical path of investigations, is anxious with specific circumstances of integrability ot the equations of movement of a unmarried inflexible physique a few fastened point,1 and with their geo metrical interpretation. This course of proposal used to be fundamental until eventually the start of the 20 th century and its so much illustrious represen tatives are L. EULER (1707-1783), J L. LAGRANGE (1736-1813), L. POINSOT (1777-1859), S. V. KOVALEVSKAYA (1850-1891), and others. bankruptcy I of the current monograph intends to mirror this department of investigations. For collateral studying at the common questions handled during this bankruptcy the reader is stated the next textbooks and experiences: A. DOMOGAROV [1J, F. KLEIN and A. SOMMERFELD [11, 1 , 1 J, A. G. 2 three GREENHILL [10J, A. grey [1J, R. GRAMMEL [4 J, E. J. ROUTH [21' 2 , 1 2 31' 32J, J. B. SCARBOROUGH [1J, and V. V. GOLUBEV [1, 2J.