Algebra and Galois Theories

Galois theory has such close analogies with the theory of coatings that algebraists use a geometric language to speak of body extensions, while topologists speak of "Galois coatings". This book endeavors to develop these theories in a parallel way, starting with that of coatings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of the Galois theory the geometric intuition that one can have in the context of the coatings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.