Dust of Azoth is a material that can convert character Ascension materials—specifically Slivers, Fragments, Chunks, and Gemstones. These can be converted through the second tab of the Crafting Bench in any city. Each conversion costs between one to 27 Dust of Azoths, depending on the material rarity.
The Dust of Azoth is an important resource that can save you time and Resin, as it allows you to exchange materials you have a lot of for those you urgently need to build a character. It's also a great tool for beginners who may not defeat bosses of certain Elements, as exchange rates are not limited to specific Element pairs.
If you are newer to Genshin, you can complete Elemental Trials in the Adventurer's Handbook and earn free Dust of Azoth. These Elemental Trials can be found in the Temple of the Lion, and include Vaporize, Melt, Overloaded, Superconduct, Electro-Charged, Frozen, Crystallize, and Swirl. Once you've completed these Elemental Trials, you can open up your Adventurer's Handbook and claim your Dust of Azoth rewards.
You can also obtain Dust of Azoth is by purchasing them from the Stardust Exchange under Paimon's Bargains. You can purchase x10 Dust of Azoth for x5 Masterless Stardust.
The shop stocks 100 of these a month, so you can buy a maximum of 1,000 Dust of Azoths for 500 Masterless Stardusts every 30 days. However, you can only hold a maximum of 2,000 Dust of Azoths at a time.
The Dust of Azoth is occasionally available from the limited event shops, where a limited number is sold for event currency. If you need this resource and can't shell out Masterless Stardust, consider browsing the event shops every time one is active to score some Dust of Azoths while they're on sale.
Check out our How to use the Enhancement Progression Calculator for Genshin Impact to help you figure out what materials to convert with Dust of Azoth.