And-Inverter Graph (AIG)
Beginner
A way of drawing any logic using only one kind of block, AND, plus markers that flip yes to no.
Novice
A way to represent any logic using only two-input AND gates, with some connections marked as inverted (NOT). Its uniform shape makes it easy for tools to simplify.
Expert
A directed acyclic graph of two-input AND nodes whose edges may be inverted. Structural hashing merges duplicate nodes as it is built. Node count and depth roughly track mapped area and delay, and rewriting, balancing, mapping and SAT-based equivalence checking all work on it. It is the core data structure in ABC.