This book is written as a text for the standard one semester course that as usually pursued by the honours and post graduate students of various universities of India and abroad with the hope that it will open a path to the Lebesgue theory to the students. The aim of this book is to cover a basic course of Lebesgue measure and outegration which flows in a Natural motivated and simple way. Each topic in the book has been treated in the easy and lucid style.