A new, fundamental stereological principle is described which allows unbiased estimates of absolute structural quantities in arbitrarily shaped structures to be made from observations sampled in arbitrary points on independently isotropic probes. As an introduction to the principle, method(s) are described which lead to assumption-free estimates of mean volume from the usual number-distribution of particle sizes. Specifically, the estimation is unbiased when arbitrarily shaped particles are sampled with uniform probability using the dissector or one of its many modifications. A special case, of interest when observations are restricted to sections, occurs when the particles are associated with some recognizable unit, like eukaryotic cells in biology. The estimation may then be carried out on a few sections of unknown thickness, or--under verifiable assumptions--on just one random section.