Preface

Among the natural sciences, the oldest is probably astronomy. Its origins date back to the rise of the first civilizations, when astronomical observations allowed for producing the first calendars. For thousands of years, cosmogonies were directly related to religious beliefs, showing a connection with the deepest questions of human heart that keep fascinating generations of modern scientists. It was not until the seventeenth century that astronomy started assuming its present aspect, thanks to the pioneers Nicolaus Copernicus, Galileo Galilei, Tycho Brahe, Johannes Kepler and Isaac Newton. It was due to their work that we understood that the orbits of celestial bodies are governed by mathematical relations; if any deviation is seen, either new, unseen objects are present to modify the equation of motion, thanks to their gravitational attraction, or a modification of the laws of gravity is necessary for some regime. An example of the first approach is the discovery of Neptune, the eighth planet of the Solar System, whose existence was hypothesized by Urbain Le Verrier and, independently, by John Couch Adams in 1846, in order to account for the anomalous motion of Uranus. Neptune was first observed by Johann Galle and Heinrich d’Arrest of the Berlin Observatory on 23 September of the same year, the same night when Galle received a letter from Le Verrier asking to confirm his predictions. Neptune was found within 1 of the predicted location, providing a strong confirmation of the laws of celestial mechanics. The second approach proved to be useful in the case of another planet, Mercury. The precession of its orbit was reported by Le Verrier himself, who pointed out in 1859 that its characteristics were at odds with the Newtonian laws of gravitation. His faith in Newtonian mechanics, and the success with Neptune, suggested him that the solution could be a new unseen planed (which he named Vulcan) or a series of smaller “corpuscules”. These attempts proved to be unsuccessful, and the explanation was finally provided by Albert Einstein in 1916, with the introduction of the theory of General Relativity. The problem of DM is conceptually not different from that of the motion of planets in the Solar System. A number of anomalies were observed, starting back in 1933, from the galactic scales to that of the largest structures, that can be explained only by the existence of some new non-luminous component which constitutes