This book is primarily written for undergraduate Mathematics Honours students of Indian Universities. Hopefully it will be useful also for Physics Honours and Engineering students. Different ideas and concepts are clearly explained in simple language and many important problems have been solved to facilitate the understanding of the concepts explained in the text. Each chapter is concluded with an Exercise comprising various interesting problems. Students may test their level of understanding by attempting to solve the problems. The chief purpose of this book is to present the concept of vector, its algebra and calculus with application to many geometrical problems, trigonometrical identities and problems on Mechanics in a systematic way so that students can grasp the ideas enunciated very easily. Apart from vector Analysis, ideas of tensor, its algebra and introductory part of its calculus is elaborated with motivation of study of tensor and its application to various branches of Applied Mathematics and Physics.