This book encourages readers to develop an intuitive understanding of the foundations of Linear Algebra. An emphasis on the concepts of Linear Algebra and Matrix Theory conveys the structure and nature of Linear Spaces and of Linear Transformations. Almost every chapter has three sections: a lecture followed by problems, theoretical and mathematical enrichment, and applications to and from Linear Algebra. Specific chapter topics cover linear transformations; row reduction; linear equations; subspaces; linear dependence, bases, and dimension; composition of maps, matrix inverse and transpose; coordinate vectors, basis change; determinants, …l-matrices; matrix eigenvalues; orthogonal bases and orthogonal matrices; symmetric and normal matrix eigenvalues; singular values; and basic numerical linear algebra techniques. For individuals in fields related to economics, engineering, science, or mathematics.