We will start with the study of the algebraic structure where the problems will be described, with the notion of supergroup. Supergroup theory allows to reconsider in an original and more general setting classical problems known in groups. A central aspect is the problem of infinite dimensional representation theory, which will lead to the analogous of the Harish-Chandra theory in this setting. On the harmonic analysis side, a general theory of the Peter-Weyl type theorems in the context of Lie supergroups could be extremely interesting for its many applications. There is an intriguing relation between the unitary representations on the supercircle and the theory of SUSY 1-curves, which is fundamental in superstring theory. Understanding its deep meaning and its higher dimensional generalization will lead to super harmonic analysis.