The course provides a rigorous introduction to Gaussian Free Fields, a universal object which occurs in various areas of mathematics (e.g., scaling limits of discrete dimer models) and physics (e.g., QFT). More in detail, the lectures will cover the following topics: construction and properties of Discrete (Fractional) Gaussian Fields; construction and properties of the continuous (Fractional) Gaussian Fields; convergence results and scaling limits. References: Lodhia et al., Fractional Gaussian fields: A survey; Sheffield, GFF for mathematicians; Biskup, Extrema of the 2d discrete GFF.