The paper is dedicated to the memory of S.V. Kovalevskaya (1850-1891), whose 150th Jubilee Anniversary was celebrated in January 2000. She was an outstanding Russian scientist-mathematician, writer, publicist, the world's first female professor, and elected Corresponding Member of Russian Academy of Sciences. We discuss here the part of her scientific heritage concerning Classical Mechanics (so called Kovalevskaya's gyroscope rotation theory) and Celestial Mechanics (Saturn's rings shapes).