The publisher recently asked me to write an overview of the most common subjects in a first course of Calculus at university level. I have been very pleased by this request, although the task has been far from easy. Since most students already have their recommended textbook, I decided instead to write this contribution in a totally different style, not bothering too much with rigoristic assumptions and proofs. The purpose was to explain the main ideas and to give some warnings at places where students traditionally make errors
