This project discusses different techniques and algorithms used to solve the parameterized Vertex Cover problem. A vertex cover of a graph G(V,E) is a subset of vertices V such that for every edge (u, v) ⊆ E, at least one of the vertices u or v is in the vertex cover. The best algorithm for this problem is known to run at O(1.2852k + kn). The optimal solution is intractable, thus optimization strategies in solving the vertex cover problem are brought off-the-shelves, including pre-processing, kernelization, and branching methodologies. A performance bound is considered for approximation algorithms listed in this research.-This project discusses different techniques and algorithms used to solve the parameterized Vertex Cover problem. A vertex cover of a graph G(V,E) is a subset of vertices V such that for every edge (u, v) ⊆　E, at least one of the vertices u or v is in the vertex cover. The best algorithm for this problem is known to run at O(1.2852k+ kn). The optimal solution is intractable, thus optimization strategies in solving the vertex cover problem are brought off-the-shelves, including pre-processing, kernelization, and branching methodologies. A performance bound is considered for approximation algorithms listed in this research.