I spent some time reviewing Aztec’s docs.

First of all, they have one of the best resources for explaining concepts and fundamentals. Kudos to the team! 

My initial thought is that there are hundreds of possibilities for building novel applications with Aztec.

Researcher at Clave and
Co author of EIP-7212 

Partial notes seemed a great feature to me. Maybe I’m misunderstanding it, but it appears to be the best way to build intent-based applications (e.g., on-chain order books).

Why?

You simply commit how much of an asset you can offer for the token you want to trade, and a counterparty can see it (since it can be decrypted, and you only prove that you own the asset you want to trade) and then fill the order.

Only one transaction is needed, and the orders are gasless. I’m not sure if we can decline a partial note, but still, this is just an example.