Tensors are not only necessary to characterize physical quantities but also to define the intrinsic properties of the medium. Tensors allow a degree of compactness to be introduced into the complex physical relationship so that relationship can be seen more clearly. Tensors can be considered as a most powerful language and mode of presentation for physical science. The aim of this book is to provide the reader a clear understanding of what the tensors are, their Algebra, Calculus and their applications? The book is divided into two parts. Part I covers the basic concepts of algebra and calculus of the tensor. Part II deals with the applications of tensors to various branches like Geometry, Mechanics, Elasticity, Electromagnetic Theory and Polarization.