In number theory, the theory of heights is a way to quantify the "arithmetic complexity" of numbers, or more generally of points on varieties. For example, even though the rational number 100001/123456 is not large, you still need a large number of bits to store it exactly in a computer, because of the large numerator and denominator. In this talk, I will develop the basics of height theory, discussing heights on $\mathbb{P}^n$, the Northcott property, the Weil height machine, and Neron—Tate heights for abelian varieties. This is a prelude to the following week's talk...