The content of this tutorial is the theoretical substantiation of the issues of determining the dependencies of linear and angular magnitudes, providing the fundamental basis of calculations for firing and controlling artillery fire .. The issues of studying the methods of preparation and performance of various fire tasks are considered. The essence and sequence of execution of fire tasks are disclosed, the order of calculation of values and norms of time of execution of fire task is shown, as well as the values and norms of possible deviations (errors). are determined. In addition, the training manual offers options for the analysis of fire problems and demonstrates examples of their solution. It is intended for students of military departments (faculties) of universities studying on specialization "'Land Artillery'"