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...Lecture notes for the algebraic geometry course held by rahul pandharipande endrit fejzullahu nikolas kuhn vlad margarint nicolas muller samuel stark lazar todorovic july contents references ane varieties morphisms of projective and ii veronese embedding n linear maps hypersurfaces in p quadratic elliptic functions cubic curves intersections lines with products segre four quadrics grassmannian incidence correspondence irreducibility images quasi under dened polynomials equal degrees i bezout s theorem resultant pythagorean triples riemann hurwitz formula points space rational tangent spaces blow up dimension sheaves schemes good topics here harris springer hartshorne chapter but also beginning shafarevich basic atiyah macdonald commutative algebra anevarieties this we mainly consider it is worth noting that several denitions related to are formally similar those involving c manifolds local analysis whereas dierential calculus following take complex eld be underlying one could any algeb...