The aim of the script is to act as a course on Scheme theory from the internal perspective
 of the topos Sh(X), therefore showing that the internal logic of sheaf topoi is a strong
 enough foundation to build the whole theory on without necessarily referring back to the
 usual methods.
 In this thesis we define what it means to work from the internal perspective:
 We define elementary topoi and how to build and interpret formulas in the internal
 logic.
 After, we move to the specific case that is the category of sheaves on either a topological
 space or a locale, and explicit the semantics of that language.
 Weshow that the logic is intuitionistically solid and prove some results about geometric
 formulas that apply to later constructions.
 When that is done, we procede to rebuild some theory of schemes from this perspective:
 First we define abelian groups, rings, local rings and modules over sheaves, and some
 special cases.
 Then we build the basics of scheme theory by defining affine schemes, general schemes,
 coherent modules, and some special classes of morphism of schemes,
 In the end we attempt to talk about relative schemes from this perspective and what
 is needed to build the theory, then procede to show that it is well suited for a synthetic
 approach to schemes through some exercises from Hartshorne’s Algebraic Geometry
 chapter II