This book, consisting of five chapters, contains 244 problems in linear algebra. The topics covered are: systems of linear equations, vector spaces, linear transformations, linear, bilinear and quadratic forms, Euclidean vector spaces and convex sets. Each chapter is divided into four parts: definitions and basic results (I), solved problems (II), additional problems (III), hints and answers for additional problems (IV). There is a table of contents, bibliography and an index, which permit easy location of a special topic and also a quick access to the hints and solutions. The book is mainly addressed to undergraduate students in mathematics as a companion and complement to the basic course in Linear Algebra, but may also be a valuable tool for the undergraduate and graduate students in engineering, computer science, economics and the natural sciences.