  In this work we present some general categorial ideas on Abstract Elementary
Classes (AECs) %\cite{She}, inspired by the totality of AECs of the form
$(Mod(T), \preceq)$, for a first-order theory T: (i) we define a natural notion
of (funtorial) morphism between AECs; (ii) explore the following constructions
of AECs: "generalized" theories, pullbacks of AECs, (Galois) types as AECs;
(iii) apply categorial and topological ideas to encode model-theoretic notions
on spaces of types %(see Michael Lieberman Phd thesis) ; (iv) present the
"local" axiom for AECs here called "local Robinson's property" and an
application (Robinson's diagram method); (v) introduce the category $AEC$ of
Grothendieck's gluings of all AECs (with change of basis); (vi) introduce the
"global" axioms of "tranversal Robinson's property" (TRP) and "global
Robinson's property" (GRP) and prove that TRP is equivalent to GRP and GRP
entails a natural version of Craig interpolation property.
