A variety of methods are currently available for creating multiple alignments, and these can be used to define and characterize families of related proteins, such as the globins or the immunoglobulins. We have developed a method for using a multiple alignment to identify an average structural "core", a subset of atoms with low structural variation. We show how the means and variances of core-atom positions summarize the commonalities and differences with a family, making them particularly useful in compiling libraries of protein folds. We show further how it is possible to describe the rotation and translation relating two core structures, as in two domains of a multi-domain protein, in a consistent fashion in terms of a "mean" transformation and a deviation about this mean. Once determined, our average core structures (with their implicit measure of structural variation) allow us to define a measure of structural similarity more informative than the usual root-mean-square (RMS) deviation in atomic position, i.e. a "better RMS." Our average structures also permit straightforward comparisons between variation in structure and sequence at each position in a family. We have applied our core-finding methodology in detail to the immunoglobulin family. We find that the structural variability we observe just within the VL and VH domains anticipates the variability that others have observed throughout the whole immunoglobulin superfamily; that a core definition based on sequence conservation, somewhat surprisingly, does not agree with one based on structural similarity; and that the cores of the VL and VH domains vary about 5 degrees in relative orientation across the known structures.