Abstract acceleration is a method that computes the precise abstract effect of loops wherever possible and uses widening in the general case. Thus, it improves both the precision and the efficiency of the analysis. % This article gives a comprehensive tutorial on abstract acceleration: its origins in Presburger-based acceleration including new insights w.r.t. the linear accelerability of linear transformations, methods for simple and nested loops, recent extensions, tools and applications, and a detailed discussion of related methods and future perspectives.