Interesting to see it posted on HN. My favourite book on the subject is Branching Programs and Binary Decision Diagrams by Ingo Wegener: https://doi.org/10.1137/1.9780898719789.

There have been recent exciting developments of the same underlying idea for more complicated data structures (consisting in syntactic restrictions of Boolean circuits) with applications to other domains in computer science. This is known as "knowledge compilation" where the original goal is to transform a knowledge base offline to represent it to a more tractable data structure efficiently supporting "online" queries such as model counting and conditioning.

See for example some of the knowledge compilers listed here http://beyondnp.org/pages/solvers/knowledge-compilers/ for Boolean functions, applications to databases with so called factorized databases https://fdbresearch.github.io/index.html.