In this work, we put forward a brief introduction to local second order elliptic operators, based on the classical literature or modern approaches to it, such as [1] [2]. My own master thesis was also used to supply some results. Our object of study are operators that in a sense behave like the Laplacian operator and some of its variants. We present a number of elementary properties and establish an Alexandroff-Bakelman-Pucci estimate. As an application, we examine symmetry results for solutions of elliptical problems.