This all-inclusive text introduces undergraduate students to the basics of linear vector spaces, tensor analysis especially, Cartesian and general tensors. The aim of this book is to specifically explain the fundamentals of tensors and their applications to mechanics, and elasticity in a consistent manner. The contents of the book provide insights of all the major topics of the tensors analysis, viz., transformations of coordinates, Einstein summation convention, Quotient law, isotropic tensor, moment of inertia tensor, metric tensor and Minkowski space. Wherever needed a short summary of the fundamental knowledge has been provided. This book covers the syllabus of various institutions which offer a course in Mathematical Physics. It also prepares the students to solve various problems of physics using Scilab programming.