Computing the solution to Least Squares Problems is of great importance in a wide range of fields ranging from numerical linear algebra to econometrics and optimization. This paper aims to present numerically stable and computationally efficient algorithms for computing the solution to Least Squares Problems as Normal equations, QR Factorization, Singular Value Decomposition. In order to evaluate and compare the stability and efficiency of the proposed algorithms, the theoretical complexities and numerical results have been analyzed.