Plane algebraic curves and Bezout's Theorem

In this thesis we study plane algebraic curves over an algebraically closed field k in the affine and projective planes. We discuss regular and rational k-valued functions on a plane curve. We follow with a discussion of the multiplicity of a point on a curve.; We look at the intersection of algebraic curves on the affine and projective planes and develop the concept of the intersection number of two curves. We follow with the statement and proof of Bezout's Theorem.