Since its first publication in 1943, it was considerably expanded and it soon became a "classic" and highly regarded reference for mathematicians, scientists and engineers.

One of the valuable characteristics of Gradshteyn and Ryzhik compared to similar compilations is that most listed integrals are referenced.

Another advantage of Gradshteyn and Ryzhik compared to computer algebra systems is the fact that all special functions and constants used in the evaluation of the integrals are listed in a registry as well, thereby allowing reverse lookup of integrals based on special functions or constants.

On the downsides, Gradshteyn and Ryzhik has become known to contain a relatively high number of typographical errors even in newer editions, which has repeatedly led to the publication of extensive errata lists.

Earlier English editions were also criticized for their poor translation of mathematical terms[1][2][3] and mediocre print quality.

[6][nb 2] While some contents were original, significant portions were collected from other previously existing integral tables like David Bierens de Haan's Nouvelles tables d'intégrales définies (1867),[6][7] Václav Jan Láska's Sammlung von Formeln der reinen und angewandten Mathematik (1888–1894)[6][8] or Edwin Plimpton Adams' and Richard Lionel Hippisley's Smithsonian Mathematical Formulae and Tables of Elliptic Functions (1922).

[nb 4] The third edition (1951) was worked on by Gradshteyn,[13] who also introduced the chapter numbering system in decimal notation.

[6][nb 2] Therefore, the fourth (1962/1963) and fifth (1971) editions were continued by Yuri Veniaminovich Geronimus (Russian: Юрий Вениаминович Геронимус, German: Juri Weniaminowitsch Geronimus)[6][nb 5] and Michail Yulyevich Tseytlin (Russian: Михаил Ю́льевич Цейтлин, German: Michael Juljewitsch Zeitlin).

[22] It was partially based on the fifth English edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and meant as an companion, but written to be more accessible for students and practitioners.