The aim of this book is to provide a sufficient mathematical background oriented towards applications in various professional fields. The authors approached this goal touching different topics, from vector geometry to differential calculus, from linear systems of equations to geometric transformations, always using a simple mathematical language, not pedantic but never superficial. This book is mainly addressed to undergraduate students with particular focus on degree courses in architecture and industrial design. In this second edition some problems have been approached through numerical techniques and the relevant software code is presented. Moreover, the readability of pictures has been improved and additional exercises are proposed.