The Alfonsine Tables were compiled during the second half of the 13th century in Toledo, Spain, and were largely diffused throughout Europe, mainly via Paris. They became the basic computing tool for European astronomers during several centuries. The Tabulae resolutae are a particular form of presenting the Alfonsine material which differs in many ways from that in the first printed edition of the Alfonsine Tables (Venice, 1483). This paper focuses on the influence of the 15th century Viennese astronomer John of Gmunden on the genesis of the Tabulae resolutae , and analyses its contents and impact on European astronomy.