Abstarct: In this thesis, the development and analysis of conjugate gradient methods for solving large-scale systems of linear and nonlinear equations are investigated. The main objective is to present an efficient algorithm with global convergence property and high convergence rate. First, the theoretical foundations of the conjugate gradient method for solving linear sys- tems with symmetric positive definite coefficient matrices are reviewed. Subsequently. the extension of this method to nonsymmetric matrices as well as problems with multi- ple right-hand sides is presented. The application of these methods in solving nonlinear problems within the Newton-Raphson frxamework is also analyzed. Then, a three-term inertial conjugate gradient algorithm of Polak-Ribière-Polyak (PRP) type, named ITTPRP, is introduced. This algorithm incorporates an inertial extrapolation step into the structure of the three-term PRP algorithm. The key feature of the proposed algorithm is that the search direction possesses both sufficient descent and trust region properties. The line search rule employs a derivative-free technique, eliminating the need for Jacobian matrix computation. Under appropriate assumptions, the global convergence of the proposed algorithm is estab- lished. Numerical results obtained from implementing the algorithm on a set of benchmark problems demonstrate the superiority and competitiveness of the ITTPRP method com- pared to existing similar algorithms. In particular, the use of the inertial extrapolation step significantly reduces the number of iterations required for convergence.