Tutorial prepared by Candidate of Technical Sciences, Associate Professor E. G. Gienko at the Department of Astronomy and Gravimetry of the Siberian State Geodetic Academy . The textbook contains theoretical concepts, positions and conclusions that constitute a mathematical apparatus for solving problems of astrometry and geodetic astronomy. Astrometry and geodetic astronomy were singled out as separate disciplines from the section “Practical Astronomy”.. A detailed description of the solution of the problems of these disciplines is given in the relevant sections. Approved by the Department of Astronomy and Gravimetry and recommended for publication by the Educational and Methodological Commission of the Institute of Geodesy and Management of the Siberian State Geodetic Academy .