In the first chapter (Algebraic Structures), the concepts of operation, group, ring, and field are presented.

In the second chapter (Matrices), the basic concepts related to matrices, types of matrices, as well as their operations are discussed.

In the third chapter (Determinants), the concept of determinant and inverse matrix is introduced, along with a detailed discussion on elementary row operations on matrices.

In the fourth chapter (Linear Systems), the fundamental methods for solving linear systems are provided, with an emphasis on the Gauss elimination method.

In the fifth chapter (Vector Spaces), the concepts of vector space and subspace, linearly independent and dependent vectors, as well as the basis and dimension of a vector space are given.

In the sixth chapter (Linear Functions), the concept of linear function and its representation with a matrix is presented, along with the concept of linear form and dual space.

In the seventh chapter (Characteristic Quantities), characteristic vectors, eigenvalues, and the characteristic polynomial of a linear transformation or matrix are introduced, along with their properties. Additionally, the concepts of polynomials and functions of a matrix are referenced.

In each chapter, many examples are solved for the understanding of all the concepts developed. Moreover, representative exercises are included, which are briefly solved at the end of the book. Finally, the book contains a glossary of terms covering all concepts of Linear Algebra.

[Excerpt from the text of the preface]