This special issue is devoted to the Mathematical Analysis of Algorithms, which aims to predict the performance of fundamental algorithms and data structures in general use in Computer Science. The simplest measure of performance is the expected value of a cost function under natural models of randomness for the data, and finer properties of the cost distribution provide a deeper understanding of the complexity. Research in this area, which is intimately connected to combinatorics and random discrete structures, uses a rich variety of combinatorial, analytic and probabilistic methods.