The book presents basic results in Algebra and Linear Algebra. It needs no prerequisites except some knowledge of set theory and number systems. The initial chapters cover the topics such as Groups, Rings and Vector spaces usually taught at the undergraduate level. The latter chapters contain some additional topics such as modules, structure theorems. Galois theory, canonical forms and quadratic forms which are taught at the postgraduate level. The topics have been presented in a simple, clear and coherent style with a number of examples and exercises. Proofs have been made direct and simple, omitting irrelevant details. The book has evolved out of teaching over a period of years and can serve as a textbook on Algebra as well as Linear Algebra