This Special Issue would collect main ideas about how algebraic equations meet Galois Theory and what mathematical instruments of this theme of research can act for the resolution of algebraic equations. In this context, the study of Galois groups and symmetric polynomials. Then, permutation groups and properties describe polynomial equations, solvable by radicals and the roots may express by a formula involving only integers and the four basic arithmetic operations. The constructions of regular polygons could be added in this collection of multidisciplinary research. It is also possible to deal with generalizations and extensions of Galois Theory, namely, to expose results on Galois connections and Grothendieck’s Galois theory as applications to classical problems.Starting from symmetric functions, we will encounter typical historical geometric problems challenging mathematics worldwide. These topics assume great modern importance through the field theory, the inverse Galois problem and inseparable extension concepts. Finally, differential graded algebras intertwine in deformation theory, fascinating elementary algebraic equations.