The study or science of riddles, enigmas, and puzzles; scholarly investigation of mysterious or obscure things.
From enigma + -ology (study of, from Greek logos 'word' or 'knowledge'). Modern scholarly term combining Greek roots.
Enigmatology as a formal study is incredibly rare—there's no 'Department of Enigma Studies' at universities—but the principles of how humans create and solve puzzles are studied in psychology, linguistics, and computer science separately.
Complete word intelligence in one call. Free tier — 50 lookups/day.