Let $G$ be a finite group and $N\subseteq G$. The set $R\subseteq G$ with $|R|=k$ is called a ``relative difference set of order $k-\lambda$ relative to the forbidden set $N$'' if the following properties hold: \beginlist%ordered{(a)} \item{(a)} The multiset $\{ a.b^{-1}\colon a,b\in R\}$ contains every nontrivial ($\neq 1$) element of $G-N$ exactly $\lambda$ times. \item{(b)} $\{ a.b^{-1}\colon a,b\in R\}$ does not contain any non-trivial element of $N$. \endlist Let $D\subseteq G$ be a difference set, then the incidence structure with points $G$ and blocks $\{Dg\;|\;g\in G\}$ is called the *development* of $D$. In short: ${\rm dev} D$. Obviously, $G$ acts on ${\rm dev}D$ by multiplication from the right. Relative difference sets with $N=1$ are called (ordinary) difference sets. The development of a difference set with $N=1$ and $\lambda=1$ is projective plane of order $k-1$. In group ring notation a relative difference set satisfies $$ RR^{-1}=k+\lambda(G-N). $$ The set $D\subseteq G$ is called *partial relative difference set* with forbidden set $N$, if $$ DD^{-1}=\kappa+\sum_{g\in G-N}v_gg $$ holds for some $1\leq\kappa\leq k$ and $0\leq v_g \leq \lambda$ for all $g\in G-N$. If $D$ is a relative difference set then ,obviously, $D$ is also a partial relative difference set. *IMPORTANT NOTE* \package{RDS} implicitly assumes that the *every* partial difference set contains the identity element (see the notion of equivalence in "RDS:Introduction" for the mathematical reason). However, the identity *must not* be contained in the lists representing partial relative difference sets. So in \package{RDS}, the difference set `[ (), (1,2,3,4,5,6,7), (1,4,7,3,6,2,5) ]' is represented by the list `[ (1,2,3,4,5,6,7), (1,4,7,3,6,2,5) ]'. And no set of three non-trivial permutations will be accepted as an ordinary difference set of `Group((1,2,3,4,5,6,7))'. For this reason the lists returned by functions like "AllDiffsets" do only contain non-trivial elements and look too short. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %E ENDE %%