Elementi di calcolo tensoriale

This is a collection of notes taken on the tensor calculus classes held at the Graduate School of Engineering "Leonardo da Vinci" at the University of Pisa from 2006 to 2011. The topics covered at lessons, aimed at providing the basic knowledge and tools necessary for the study of continuum mechanics, include fundamental results on tensor algebra and analysis. Chapter 1 provides a brief introduction to finite dimensional vector spaces. Then, Chapter 2 addresses the classical topics of tensor calculus, including symmetric and skew-symmetric tensors, the theorem of polar decomposition, fourth-order tensors, isotropic tensor functions and the differential calculus of tensor functions. The text is accompanied by numerous examples and exercises.