An Introduction to the Theory of Algebraic Surfaces : Notes by James Cohn Harvard University 1957–58 Homogeneous and non homogeneous point coordinates Coordinate rings of irreducible varieties Normal varieties Divisorial cycles on a normal projective variety V k (dim(V)=r1) Linear systems Divisors on an arbitrary variety V Intersection theory on algebraic surfaces (k algebraically closed) Differentials The canonical system on a variety V Trace of a differential The arithemetic genus Normalization and complete systems The Hilbert characteristic function and the arithmetic genus of a variety The Riemann Roch theorem Subadjoint polynomials Proof of the fundamental lemma.