The Trachtenberg system is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Russian Jewish engineer Jakow Trachtenberg in order to keep his mind occupied while being held in a Nazi concentration camp.

The rest of this article presents some methods devised by Trachtenberg. Some of the algorithms Trachtenberg developed are ones for general multiplication division and addition. Also the Trachtenberg system includes some specialized methods for multiplying small numbers between 5 and 13.

The chapter on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.