  In this essay we give a general picture about the evolution of Grohendieck's
ideas regarding the notion of space. Starting with his fundamental work in
algebraic geometry, where he introduces schemes and toposes as generalizations
of classical notions of spaces, passing through tame topology and ending with
the formulation of a geometry of forms, we show how the ideas of Grothendieck
evolved from pure mathematical considerations to physical and philosophical
questions about the nature and structure of space and its mathematical models.
