The book contains a series of essays on the interesting problems of the mechanics of space flight and celestial mechanics. They consider various trajectories of the mechanics of space flight, the evolution of the orbits of artificial and natural celestial bodies, resonance phenomena encountered, describe the original problems of the dynamics of relative motion in orbit and many other problems. A parallel presentation of the necessary mathematical apparatus is given, but the emphasis is on identifying the mathematical essence of the problems. The book is intended for anyone interested in or engaged in the mechanics of space flight, especially young professionals in this field and students of relevant specialties.