The book describes the theoretical foundations of inertial navigation and describes the main functional elements of inertial navigation systems (INS). General and particular representations of the algorithm for determining the current coordinates of the object in relation to some practically important methods of constructing the INS, their classification, analysis of errors, preparation for work, as well as issues of correction of the INS from external sources are considered. The book is based on materials from open domestic and foreign literature and is intended for engineers and scientists in the field of inertial navigation. It will also be useful for students of universities of relevant specialties.