In the 1980s, Andreas Dress introduced what are now known as Delaney-Dress symbols, building on inspiration from work of M. S. Delaney. This work gave rise to combinatorial tiling theory: a framework for describing periodic tilings not through coordinates and geometry, but through a finite, purely combinatorial object -- a small coloured graph that captures how vertices, edges, and tiles fit together, and how a tiling's symmetries act on them. Two tilings turn out to be equivariantly equivalent exactly when their Delaney-Dress symbols are isomorphic, turning a hard geometric classification problem into a tractable combinatorial one.

This talk gives a practical introduction to the theory. We build up the Delaney-Dress symbol from a tiling step by step, try to convey the intuition behind chambers, involutions, and branching numbers, and show how the symbol can be read back to recover a tiling's structure. Along the way we'll look at examples and tools used in practice, aiming to leave the audience equipped to work with Delaney-Dress symbols directly, rather than just recognizing the name.