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.

• Satisfiability: Theory, Practice, and Beyond Boot Camp
• Beyond Satisfiability
• Theoretical Foundations of SAT/SMT Solving
• 50 Years of Satisfiability: The Centrality of SAT in the Theory of Computing

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.