This manuscript is the lecture notes for the course of the same title I gave at the Summer school on linear logic and geometry of interaction that took place in Torino in August 2013. The aim of this course is to give a broad introduction to linear logic, covering enough ground to present many of the ideas and techniques of the field, while staying at a (hopefully) accessible level for beginners. For this reason, most technical development is carried out in the simple multiplicative fragment, with only hints at generalizations. As prerequisites, some knowledge of classical sequent calculus and some knowledge of the λ-calculus is useful.