Galois theory is a branch of mathematics that deals with the study of field extensions and their relationships to polynomial equations. Here are some possible contents for a Duolingo-like website dedicated to Galois theory:

Introduction to field extensions: This could include lessons on what field extensions are, how they are used to solve polynomial equations, and the concept of Galois groups.

Solving polynomial equations: Lessons in this section could cover techniques for solving polynomial equations, such as the quadratic formula, synthetic division, and the factor theorem.

Galois groups and field extensions: This section could delve into the concept of Galois groups and how they relate to field extensions. It could also cover the role of Galois groups in determining the solvability of polynomial equations.

Applications of Galois theory: This section could explore the various applications of Galois theory in areas such as cryptography, number theory, and algebraic geometry.

Practice exercises: Throughout the website, there could be a variety of practice exercises and quizzes to help users test their understanding of the material.

Additional resources: The website could also include links to additional resources, such as textbooks, lectures, and articles, for users who want to learn more about Galois theory.