This essay examines some aspects of the teaching of mathematics and its applications in three of the principal sixteenth century Spanish universities (Salamanca, Valencia and Alcala) and in other institutions sponsored by the monarchy, such as the "Casa de la Contratacion" (House of Trade) of Seville and the so-called Academy of Mathematics of Madrid. All three of the above universities had chairs of mathematics. In the "Casa de la Contratacion" and other nautical schools the teaching of mathematics was oriented toward providing the foundations of navigation (nautical astronomy, instruments and maps, etc.). The Academy of Mathematics was oriented mainly towards subjects related to cosmography and navigation. Although the different areas of the teaching of mathematics imposed conditions on the discourses and practices of the mathematical disciplines, they did not impede the circulation of persons, knowledge, and practices among these areas.