ABSTRACT
At the beginning of the twentieth century the general idea of the structures underlying diverse mathematical theories became completely conscious and, as a consequence, led to a remodeling and deepening of most of these theories, underscoring more and more the deep unity of mathematics. Algebraic geometry is one of the principal beneficiaries of these tendencies; its relations with the theory of analytic functions, on the one hand, and with algebra and number theory, on the other, are expanded considerably, enriching it with a multitude of new points of view. One of the effects of this expansion will be to erode, little by little, the rigid framework of the projective and birational methods, and to prepare the way for a much more flexible and more general concept.
