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Many significant real-life problems are modelled using the tools and techniques of Linear Algebra. In recent years Linear Algebra has become an essential part of Mathematics, Engineering, Computer science, Physics, Economics, Statistics and many other subjects. This book for linear algebra caters to the need of undergraduate and postgraduate students who take Linear Algebra and also others regardless of their field of specialization. The emphasis is on the concept of vector space and linear transformation. Mathematical structures can be used to model the world around us. The topics covered in the book for linear algebra is as follows: Chapter 1 deals with preliminaries required to understand the topics in the book Chapter 2 is an introduction to vector spaces, subspaces, linear span and sum and direct sum of the subspaces. In chapter 3 basis, dimension, dual space and inner product space. Chapter 4 deals with linear transformations, Rank and nullity, algebra of linear transformation, Chapter 5 is devoted to characteristic polynomials, invariant subspaces, projections, linear operator on inner product spaces. In Chapter 6, Matrix algebra, Rank and Nullity of matrix, Change of basis, similarity of linear transformation and Spectrum. In Chapter 7, we discuss modules, sub-modules, quotient modules, homomorphism of modules and cyclic modules. The book is easy to understand; plenty of examples have been provided to clarify the concepts. Theorem and problem proof style stimulates the student to think deeply about the subject.