  We study the notion of formal self duality in finite abelian groups. Formal
duality in finite abelian groups has been proposed by Cohn, Kumar, Reiher and
Sch\"urmann. In this paper we give a precise definition of formally self dual
sets and discuss results from the literature in this perspective. Also, we
discuss the connection to formally dual codes. We prove that formally self dual
sets can be reduced to primitive formally self dual sets similar to a
previously known result on general formally dual sets. Furthermore, we describe
several properties of formally self dual sets. Also, some new examples of
formally self dual sets are presented within this paper. Lastly, we study
formally self dual sets of the form $\{(x,F(x)) \ : \ x\in\mathbb{F}_{2^n}\}$
where $F$ is a vectorial Boolean function mapping $\mathbb{F}_{2^n}$ to
$\mathbb{F}_{2^n}$.

Combinatorics