There are numerous resources available to learn about the theoretical and practical aspects of SAT.

In 2021, there was a bootcamp and several workshops related to SAT at the Simons Institute.

All lectures were recorded and are freely available to watch.

A nice way to get started with practical SAT solving is to watch Armin Biere’s SAT solving lectures from the bootcamp.

It explains how to build Satch, a SAT solver in C written from scratch.