Introduction and Preliminaries Background: Familiarity with basic PDE theory (for example Harmonic functions, max principle...) and basic facts about Sobolev Spaces.

Holder regularity of weak solutions to divergence and non-divergence elliptic equations. (II) De Giorgi- Nash-Moser Theorem. Background: Familiarity with basic PDE theory (for example Harmonic functions, max principle...) and basic facts about Sobolev Spaces.