Mathematics and Astronomy walked together for thousands of years. Ptolemy, Copernicus, Galileo, Kepler, Newton are good examples of this fruitful interaction between both disciplines. In medieval educational theory, the "quadrivium" consisted of arithmetic, geometry, music, and astronomy, which prove their common past in the development of science. More recently, the extraordinary works by Einstein with the General Theory of Relativity give new insights to our vision of the universe, in a wonderful cooperation of geometry and physics. This book collects the recent results presented in the Symposium Mathematics and Astronomy: A Joint Long Journey, celebrated last November 2009 in Madrid, Spain, to show and stress these links with the occasion of the celebration of the International Year of Astronomy IYA2009.