[en] This paper considers the main elements of convex analysis in infinite-dimensional spaces, that is the most essential properties of convex functions valued in anti R (the extended real numbers) such as: continuity property, duality, sub-differentiability, properties concerning the minimization of such functions, and, finally, the connections of these with the monotonic-operators theory and the variational-inequalities theory. Convexity has always played a fundamental role in the study of variational problems, but systematic studies on convexity have been carried out only in recent times. (author)