A Grothendieck topology can be regarded as a topology on a category. This notion generalizes the usual notion of topology on a space and has applications in various contexts. After a quick sketch of the relevant notions in category theory and some illustrative examples, I will give an intuitive introduction to Grothendieck topologies. Some explanatory pictures will be drawn, and we discuss some commonly used examples and some artificial ones. The notion of sheaves and elementary topoi then follow. If time permits, I will also touch some points of hypercoverings, which can be viewed as "higher coverings".