"The Development of Arabic Mathematics: Between Arithmetic and Algebra" offers a comprehensive analysis of the developments in Arabic mathematics between the 9th and 15th centuries. This scholarly book brings together over ten studies that focus on one of the most significant advancements in Arabic mathematical thought, particularly the interaction between arithmetic and the algebra of al-Khwarizmi. This interaction led to the establishment of various mathematical disciplines, including polynomial algebra, combinatorial analysis, algebraic geometry, and Diophantine analysis. The author highlights these disciplines through epistemological analyses and the discovery of previously unknown materials, proposing an alternative periodization of classical mathematics. The results of these studies have already gained recognition among historians of Arabic mathematics and have been integrated into their current publications. The English translation of this work is particularly valuable for historians and philosophers of mathematics and science.