Newton polygon relative to an arc We give an elementary introduction to the singularity theory of complex polynomials of two variables. Let P(x,y) be such a polynomial, P(0,0)=0. Newton showed how to find the solutions y(x) of the equation P(x,y(x)) = 0, using the (Newton) polygon method. We generalize this construction to study the polar curves, Lojasiewicz exponents, singularities at infinity, and equi-singular deformations. (707A, August, Wednesday 12, 19, 11-12, and Wednesday 26, 11-13) These lectures are mainly designed for students.