This book presents the Determinant theory with the use of hypercomplex Grassmann figures.It simplifies the proof of many determinant features.It also states several ways of solutions of linear algebraic systems, most of which are connected with the Determinant theory.The teaching experience in technical universities has demonstrated that the suggested way of presenting the Determinant theory is understood more easily.The title of the book is explained by a desire to attract readers’ attention to the well-known in the algebra sphere while introducing a new and more convenient way to present the Determinant theory for technical universities.