1610s, "discussion, debate" (a sense now obsolete), from Late Latin dissertationem (nominative dissertatio) "discourse," noun of action from past-participle stem of Latin dissertare "debate, argue, examine, harangue," frequentative of disserere "discuss, examine," from dis- "apart" (see dis-) + serere "to join together, put in a row, arrange (words)," from PIE root *ser- (2) "to line up."
Sense of "formal, written treatise" is from 1650s. Meaning "research paper required as a final project for a Ph.D or other doctoral degree" is attested by 1877 in reference to continental universities; it was in use in the U.S. by 1890. Related: Dissertational. There is no regular verb to go with it: Dissert (1620s, from French disserter, from Latin dissertare) is obsolete, and dissertate (1766) is marked "Unusual" in OED.