The book contains a series of essays on interesting problems of space flight mechanics and celestial mechanics; they consider various trajectory problems of space flight mechanics, the evolution of the orbits of artificial and natural celestial bodies, resonant 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 mechanical essence of the problems. The book is intended for anyone interested in or involved in the mechanics of space flight, especially young professionals in this field and students of relevant specialties.