Which neurotransmitters are linked with substance abuse disorder?

Many: Substance abuse dysregulates all neurotransmitters, in some way -- and different drugs may hit on different ones more than others. But possibly Dopamine is the one most central. Dopamine is known to have significant function in the brain's reward center. "dopamine rush" in this reward center contributes strongly to addiction potential in a drug.

Depends on drug: Dopamine, serotonin are affected by stimulants like cocaine, meth. Endorphins affected by downers like heroin, opioids. Gaba affected by benzo.