we provide of comparison of different concepts of "smallness" of sets and operators which frequently occur in real analysis, measure theory, functional analysis, and operator theory. Typical examples are nullsets, sets of first category, sets of small Hausdorff dimension, and sets which are "small" from some metric or topological viewpoint. The presentation is elementary and selfcontained, with a particular emphasis on examples and counterexamples, rather than abstract theorems in great generality
