Introduction to Intersection Theory

Intersection theory is a fundamental tool in algebraic geometry to study the geometry of algebraic varieties. The aim of this thesis is to provide a comprehensive and rigorous introduction to intersection theory by following William Fulton’s classic book “Intersection Theory” and the class notes of Ravi Vakil. Starting from the definition of the Chow ring and divisors, the construction of the intersection product is developed step by step through the use of Chern and Segre classes, Gysin morphisms and the deformation to the Normal Cone. To conclude, various application are presented including the Grothendieck-Riemann-Roch theorem.