The book is trying to explain the main features of Celestial Mechanics using a new technique (in this, it is very unique). Its emphasis, in terms of applications, is on the Solar System, including its most peculiar properties (such as chaos, resonances, relativistic corrections, etc.). All results are derived in a reasonably transparent manner, so that anyone with a PC and a rudimentary knowledge of Mathematica can readily verify them, and even extend them to explore new situations, if desired. The more mathematically oriented reader may also appreciate seeing quaternions as the basic algebric tool of the new approach. Practicing astronomers may also be happy to learn that the method has eliminated the problem of zero divisors, and does not require using the rather controversial averaging principle.