Introduction and Motivation
We give a mathematical introduction to percolation, and state the main questions. We introduce the various critical percolation thresholds, and argue that the most interesting behavior occurs close to it. We introduce critical exponents that describe the system at or close to the phase transition, and the role of the upper critical dimension. Finally, we explain basic techniques (in particular, the BK and FKG inequalities and Russo’s formula) and describe our aim of these lecture notes.