The convex analysis, among other possibilities, could be seen as a particular case of nonsmoorth analysis. In this context, we present the background necessary for the generalization of the concept of derivative and its properties in the case of nondifferentiable convex functions. These notes were written as a support for a short course on Convex Analysis given by Sofia Oliveira Lopes at Lab I2002, Department of Electrical Engineering Department, Faculdade de Engenharia, University of Porto in July 2011.