This is the course that will prepare the student to conduct research on 2-to-1 functions, intended as part of the thesis topic. The main materials that will be covered would be: algebraic number theory, techniques for computation of Galois groups for low degree polynomials, permutation rational function, exceptional functions and applications of 2-to-1 functions in coding theory. A large part of this course will be reading related papers. Students should seek approval from the course instructor to take this course.