The book 'The Art of War' was written by :

The book 'The Art of War' (Italian: Dell'arte della guerra) was written by the Italian Renaissance political philosopher Niccol"o Machiavelli [2]. Written between 1519 and 1520 and published in 1521, it was the only major political work by Machiavelli printed during his lifetime [1]. The work is structured as a Socratic dialogue set in a Florentine garden, where the character Fabrizio Colonna discusses military organization, training, and strategy [4]. While the title is famously shared with an ancient Chinese treatise by Sun Tzu, Machiavelli's version focuses on the creation of a modern army and the integration of military and political life [2]. Other options like Thucydides, Thomas Hobbes, and J.S. Mill are prominent political thinkers but are associated with works such as the 'History of the Peloponnesian War', 'Leviathan', and 'On Liberty' respectively.

Sources

1. [1] https://en.wikipedia.org/wiki/The_Art_of_War_(Machiavelli_book)
2. [2] https://www.britannica.com/topic/The-Art-of-War-by-Machiavelli
3. [4] https://dspmuranchi.ac.in/pdf/Blog/DPOL201_WESTERN_POLITICAL_THOUGHT_ENGLISH.pdf