In this dissertation, some modified stationary and non-stationary iterative methods for solving system of linear equations were studied. There are different techniques to modify stationary and non-stationary iterative methods. One of such methods is refinement of iterative method. Using the basic theorems and assumptions in the field of stationary and non-stationary iterative methods, refinement of Jacobi (RJ), refinement of generalized Jacobi (RGJ), refinement of Jacobi overrelaxation (RJOR), refinement of Gauss-Seidel (RGS), re finement of successive overrelaxation (RSOR), refinement of accelerated overrelaxation (RAOR), second degree refinement of Jacobi (SDRJ) and multi-parameters overrrelax ation (MPOR) were modified. Furthermore, basic theorems were developed and proved. Convergence analysis for the modified methods were shown by choosing appropriate matrices. In addition, we derived the iterative methods of linear non-stationary second degree iter ative methods based on derivation of Young’s stationary second degree iterative method. On the other hand, we introduced two theorems on cyclic Chebyshev semi-iterative methods based on 2 × 2 block SDD and 2 × 2 block H-matrices. For each modified method appropriate numerical examples and comparison of re sults with previous existing methods were examined. It is observed that, the modified methods in this study were better by considering number of iteration, spectral radius and rate of convergence