Graduate Program in Physics.Kozçaz, Can.Çark, Bilal.2023-10-152023-10-152022PHYS 2022 C37https://digitalarchive.library.bogazici.edu.tr/handle/123456789/19818In this thesis, the approaches for calculating refined topological string amplitudes on compact Calabi-Yaus for the case local P^2 are investigated. One approach is making use of large N duality and refined Chern-Simons theory (Aganagic and Shakirov) and the other is defining another vertex (Iqbal, Kozçaz). It turns out that this new vertex can be obtained from refined Chern-Simons theory using properties of Macdonald and Schur functions, in this thesis we outline the way of this derivation. Aside from a brief review of topological strings, large N duality and knot invariants that can be calculated using Chern-Simons theory, a review of topological vertex formalism and its derivation using Chern-Simons theory, both in the refined and unrefined case is included.String models.x, 49 leaves