The Traveling Salesman Problem is one of the most difficult problems in computer science and computational mathematics. A solution of an algorithm aims to find the shortest way to move through a set of locations and return to the original location in the process. This thesis aims to achieve a comprehensive analysis of the TSP by conducting a comparative analysis of existing algorithms and introducing a new algorithmic approach designed by the author to create an efficient and optimal solution. The algorithms analyzed are: Nearest Neighbor, Christofides', Ant Colony Optimization, Simulated Annealing, Genetic, Brute Force, and the original algorithm by the author.