This book is based on a course Calculus-II. The purpose of this text book is to provide a rigorous treatment of the foundations of dierential calculus. We write this book as per the revised syllabus of F.Y. B.Sc. Mathematics, revised by Savitribai Phule Pune University, Pune, implemented from June 2019. Calculus is the most useful subject in all of mathematics and it is used extensively in applied mathematics and engineering.