From the end of the 10th century, the mathematician al-Karajī founded a new school of algebraists. The school sought to investigate the relationship between arithmetic and algebra. The book Qisṭās al-mu‘ādala fīʻilm al-jabr wa’l-muqābala (Balance of the equation on the science of restoration and comparison by the mathematician al-Zanjānī (first half of 13th century) is a treatise on algebraic calculations, which clearly belongs to this tradition of arithmetical-algebraic research. It is composed of a theoretical part and two long collections of problems. In order to study these collections, we need to consider first the history of the transmission of these problems, and to analyze the continuities and discontinuities between al-Zanjānī’s collections and those of the algebraists that constituted a direct or indirect reference point for him. In addition to this heritage, the examination also reveals that it is in the problems themselves that the theory of algebraic calculations is fully expressed and put into practice. Therefore, problems show al-Zanjānī’s algebra in action. They also give the algebraist the opportunity to find new branches of his discipline, as the case of indeterminate analysis testifies. In this article, we focus on the structure of Qisṭās al-muʻādala and we examine the resolution of some of the book’s determinate and indeterminate problems.