The book introduces the concepts of skew polynomials from two commuting "variables" and conjugates to skew polynomials from one and two "variables." The linear equation with coefficients in division algebra is investigated and its general solution is found. Right and left result matrices of skew polynomial systems are constructed. Some of their properties are considered. The theorem on the relationship of the ranks of the resulting matrices with the order of their right (PNOD) and left (LNOD) largest common divisor and the smallest common multiple is proved, an algorithm for calculating the PNOD and LNOD of a system of skew polynomials, different from known algorithms, is formulated.