Shapes of biological macromolecules --- RNA, DNA, and proteins --- can be represented by abstract algebraic structures provided as suitably coarse resolution is chosen. These abstract structures, for instance partially ordered sets and permutation groups, can be used for deriving new metric distances between biomolecular shapes and for proving surprising theorems on sequence-structure relations. 1. Introduction One of the central problems in contemporary molecular biology is the comparison of biomolecular structures. The most basic question in this context is "What do we mean when we say that two structures are the same?" We argue that even this question is far from being trivial. Clearly, no two biopolymers with different sequence (primary structure) can have identical spatial conformations at atomic resolution. However, atomic resolution is not what is referred to when one says, for instance, that all tRNAs have the same shape. Of course, different levels of precision will be suitabl..