Differential Galois Theories, Linear and non-linear differential Galois theory, Abelian Varieties, Galois cohomology, Kummer theory, A-hypergeometric function, Appell function, Horn function, Euler integral, Dwork module, Multiplicity estimate, Drinfeld modular form, Drinfeld quasi-modular form, $A$-modular form, $A$-quasi-modular form, Pseudogroups,Differential Invariants, Ultrametric, irregularity, index, radius of convergence, Exponential Module, $G$-function, $q$-difference equations, formal ification, analytic ification, Newton polygon ; slope filtration ; small divisors, Tannakian categories, Unipotent radical, Galois groups, $t$-motives, Calabi–Yau manifolds, integrality of mirror maps, $p$-adic analysis, harmonic numbers, hypergeometric differential équations, integrality of mirror maps, $p$-adic analysis, Dwork's theory in several variables, harmonic numbers, hypergeometric differential équations, $p$-adic $q$-difference equations, $p$-adic differential equations, Confluence, Deformation, unipotent, $p-$adic local monodromy theorem, roots of unity, Berkovich spaces, stratifications, radius of convergence, Finite difference systems, difference Galois theory, Elliptic hypergeometric functions, elliptic gamma functions, elliptic beta integrals