The celebrated Alexandrov-Bakelman-Pucci Maximum Principle (often abbreviated as ABP estimate) is a pointwise estimate for solutions of elliptic equations, which was introduced in the 1960s. It was motivated by beautiful geometric ideas and has been a fundamental tool in the study of non-divergent PDEs. More recently, this PDE technique also pays back to geometry - the ABP estimate and its extensions can be used to prove some optimal classical geometric inequalities such as the Isoperimetric and Minkowski inequalites.