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Cosmic microwave background radiation is the residue of the great heat following the Big Bang. A tenuous sign, over 13 billion years old, in which the answers to many of the questions about the nature of our Universe are hidden. Discovered by chance in 1964, in the last forty years this fossil trace of the origins of the Cosmos has been explored with every available means. Two Nobel Prizes in physics have already been awarded for research involving it, the last in 2006 for the results of the COBE satellite. Much of the information encoded in the cosmic background radiation was impressed by the superimposition of acoustic waves present in the early Universe: a "music" of the Big Bang, which cosmologists have tried for years to reconstruct, using techniques similar to those that allow to distinguish the sound of different musical instruments. Only recently have the first notes of this extraordinary cosmic symphony finally been revealed, but the investigation is not over yet. This book illustrates, with a language suitable even for non-specialists, the theories, observations and discoveries that have brought cosmology into a new era.