Epistemology and Cognition of Mathematical Knowledge. The development of the Systems of Numbers and the Numbering Systems in Mathematics Education (From the Natural Numbers to the Limiting Processes and the Completeness of ℝ). Anatomy of the notions of Function and Limit. Aspects of the learning of Geometry (Van Hiele Levels, Visualization and the 3D v 2D paradigm). The Construction of Definitions and their role in the development of mathematical theories. Study of theoretical frameworks as Concept Image / Concept Definition, APOS. Advanced Mathematical Thinking (AMT): the introduction to Abstraction and the paradigm of Real Analysis.