We characterized the group of linear operators that preserve sign-nonsingular matrices over ��(ℝ). Then we extended these results to n show that a linear operator T that strongly preserves L-matrices over ��,�(ℝ) if and only if T preserves L-matrices and T is also one to one on m,n the set of cells. We also characterized the group of linear operators that strongly preserve L-matrices. In addition, we characterized the group of linear operators that preserve super L- matrices, the subset of L-matrix. Also we investigated linear operators that preserve totally L-matrices, the subset of L-matrix. Chapters 1 and 2 of this dissertation contain some material of the work done by other researchers on the linear preserver problems and the properties of sign-nonsingular matrices and L-matrix. Characterizations of linear operators in Chapters 3, 4, 5, and 6 of this dissertation are new.