Giving the basic definitions and explaining the some important ideas, we will introduce the field of knot theory. We will explain the relation between a knot and its diagram and how to find invariants which allow us to distinguish different knots (or links). Thanks to an easy invariant we will prove the existence of non-trivial knots! We will introduce the concept of Seifert Surface of a knot: An orientable, compact connected surface whose boundary is the knot. We will show an algorithm to create a Seifert Surface starting form an arbitrary projection of a knot. We will see that this algorithm will be useful to calculate the genus, a knot invariant, of a certain class of knots. If time will permit we will talk of the signature of a knot, its relation with the unknotting number (Gordian distance), and the general context in which Seifert was working when he introduced his surface.