The Carpet Museum is exactly what it sounds like: three floors of Azerbaijani carpets grouped by region — Tabriz, Karabakh, Shirvan, Quba, Baku, Ganja — with each style displayed alongside the tools, dyes, and looms used to make it. The labelling is good and the staff are knowledgeable enough to walk you through the symbolism if you ask.
Carpet-making is one of the things Azerbaijan does demonstrably well. The Karabakh and Shirvan rooms are the most rewarding for a casual visitor: the geometric medallions and the stylised plants and animals each have a meaning, and once you've seen a dozen of them the differences between schools become legible. Allow at least ninety minutes.