This book is outcome of the lecture notes that I have been teaching to under graduate students in Maharaja Jivajirao Shinde Mahavidyalaya, affiliated to Savitribai Phule Pune University from last fourteen years. Linear Algebra is a most important branch of mathematics. In this book I have tried my best to cover the necessary topics related vector spaces and linear transformations. It is intended to serve the needs of students studying this course at undergraduate level. The objective of this book is to introduce basics of linear algebra in a simple and easy language. The purpose of this book is to provide elementary introduction to the vector spaces and its properties. In this book reader will learn linear spaces in a simple and easy language with illustrations. I have taken a care to present the matter in a systematic way. Necessary theorems on related topics are proved in a simple language. This book also contains several solved examples for better understanding of readers. I hope that as a result of a careful study of this book, reader would have a good appreciation.