In this chapter, we expand our knowledge about vector calculus in the so-called Euclidean plane. Although the space surrounding us is three-dimensional, we are dealing with vector calculation in the plane in this chapter for simplicity reasons. The new concepts and terminologies of (two-dimensional) vector calculus can mostly be generalized one-to-one to the three- and later also to the four-dimensional case, so we refrain from the more complicated representations in three dimensions here.