In this introductory chapter, we introduce some basic concepts that are necessary for the further understanding of this book. These are the concepts of force, rigid body, reaction forces and degrees of freedom of bodies. In addition, we briefly discuss free-body diagrams and the principle of action and reaction, two aspects that are of outstanding importance in applied mechanics and which we will use in many ways in this book. The chapter concludes with a presentation of some basic relations of vector calculus as they are relevant to the contents of this book.