In this chapter, we introduce the Liouville measures associated with the continuum two-dimensional Gaussian free field (GFF). Informally speaking, for a fixed parameter γ (the so-called coupling constant), the γ-Liouville measure is obtained by exponentiating γ times the GFF and taking this as a density with respect to Lebesgue measure. Since the GFF is not defined pointwise, the rigorous construction of this measure requires an approximation procedure. The bulk of this chapter is dedicated to establishing appropriate approximations, justifying their convergence, and proving uniqueness of the resulting measures. We also prove an important change-of-coordinates formula. The construction will be generalised in Chapter 3, which treats the overarching theory of Gaussian multiplicative chaos measures. These are measures of the same form discussed above, but constructed from a general underlying log-correlated Gaussian field. While the two-dimensional GFF is really just a specific example of such a field, some arguments specific to the GFF can be used to simplify the presentation and introduce relevant ideas in a clean way, without the need to introduce too much machinery.