Some years ago, Coursera offered a MOOC (Massive Online Open Course) on Functional Analysis: An Introduction to Functional Analysis. Taught by John Cagnol. Ecole Centrale Paris.
The duration was 8 weeks: 1 Topology; continuity and convergence of a sequence in a topological space. 2 Metric and normed spaces; completeness. 3 Banach spaces; linear continuous functions; weak topology. 4 Hilbert spaces; The Riesz representation theorem. 5 The Lax-Milgram Lemma. 6 Properties of the Lp spaces. 7 Distributions and Sobolev Spaces. 8 Application: simulating a membrane.
Now it is possible to find the videos in the following youtube link:
https://www.youtube.com/playlist?list=PLSpInro6Ys2IHve6oN9h005zmwfLnOSp1
However, the possibilities of doing short exams, asking questions, etc. are no longer available.
Is there any comparable MOOC on Functional analysis currently active?