This chapter is devoted to the fundamentals of fine potential theory, that is, the theory of finely [hyper/super]harmonic functions on a finely open set and related problems. In Sect. 2.1, we prove an extension result (Theorem 2.1.25) and show that every finely hyperharmonic function is finely continuous. We extend the fundamental convergence theorem to finely hyperharmonic functions (Theorem 2.1.34) and prove a convergence property for sequences of finely harmonic functions on a finely open set and that the fine topology is locally connected (Corollary 2.1.33). We also prove removable singularities theorems for finely [hyper]harmonic functions. Reduction and balayage relative to a finely open set are defined and their properties are studied in Sect. 2.2.