  We investigate finite right-distributive binary algebraic structures called
shelves. We first use symbolic computations with Python to classify (up to
isomorphism) all connected shelves with order less than six. We explore the
group structure generated by the rows of \textit{latin} shelves. We also define
two-variable shelf polynomial by analogy with the quandle polynomial and then
state a conjecture about connected idempotent shelves.
