Volker Strassen's work has had enormous influence on both the theory and practice of algorithm design. He has discovered some of the most important algorithms used today on millions if not billions of computers around the world. His algorithms include fast matrix multiplication, integer multiplication, and a test for the primality of integers. In 1969 Strassen discovered a novel way to multiply two $n$ by $n$ matrices in $O(n^{2.81})$ time. This intricate yet simple algorithm is the method of choice for multiplying dense matrices of size 30 by 30 or more on machines today. Using this new matrix multiplication routine, he was able to show that Gaussian elimination is not optimal. With Bob Solovay he developed the first provably fast randomized primality test. Variants of his primality testing is used by machines on a daily basis for cryptographic methods such as RSA and for data structures such as hash tables. The primality test opened the world of probabilistic algorithms to computer scientists. For his work on primality testing and randomized algorithm he was the co-recipient of the ACM Paris Kanellakis Theory and Practice Award. The Schonhage-Strassen integer multiplication method algorithm held the world record for the fastest multiplication algorithm for thirty five years. In practice, it is still a standard tool for computing with large numbers. Besides his very practical work, Strassen has also proved fundamental theorems in statistics, including "Strassen's law of the iterated logarithm" and the principle of strong invariance. He is considered the founding father of algebraic complexity theory with his work on the degree bound, connecting complexity to algebraic geometry, and introduced fundamental notions and results in bilinear complexity and tensor rank.