An investigation into an algebraic system with a single binary operation, called a skew-group, based on axioms of associativity; skew-commutativity (x+y+z=x+z+y); right identity; and left inverse. Definitions are given for left coset, quotient skew-group, homorphism, kernel, and subnormal skew-subgroup. Theorems are proved analogous to the Fundamental Homomorphism, First and Second Isomorphism, and Zassenhaus Theorems, for group theory.