This book is devoted to the basic topics of linear algebra and module theory. The first six chapters contain an account of the most important topics in ordinary linear algebra, written for the reader who needs to be prepared for study of advanced subjects like Lie algebras, group theory, functional analysis, operator theory, and geometry as well as subjects in applied mathematics and theoretical physics. The remaining eight chapters provide a more abstract but a modern introduction to the fundamental concepts of linear algebra. The reader learns how to derive canonical forms of linear operators over finite dimensional vector spaces using general theory of modules over principal ideal domains and how to extend basic ideas of linear algebra to more abstract concepts of Noetherian, Artinian, semisimple, free, projective, and injective modules.

Mohammad Shahryari joined Sultan Qaboos University (SQU) as an assistant professor in August 2019. Before that, he was a faculty member of mathematical sciences, University of Tabriz, Iran. There, he started his career as an assistant professor in 2000, then he was promoted to the rank of associate professor in 2008, and to the rank of full professor in 2015. His research focus has been on pure mathematics, especially in the field of Group Theory (Geometric and Combinatorial Group Theory). The main research area in this branch is Algebraic Geometry over Groups and Universal Algebras, where the connections between algebraic structures and logical aspects of groups and general algebraic systems are studied.