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The present work is intended to be an introduction to the Superposition Theory of David Carfì. In particular I shall depict the meaning of his brand new theory, on the one hand in an informal fashion and on the other hand by giving a formal approach of the algebraic structure of the theory: the S-linear algebra. This kind of structure underpins the notion of S-spaces (or Carfì-spaces) by defining both its properties and its nature. Thus I shall define the S-triple as the fundamental principle upon which the S-linear algebra is built up.