baseball cap, beret, billycock [British], biretta, boater, bonnet, bowler, calotte, capuche, casque, castor, cloche, cocked hat, cowboy hat, cowl, derby, fedora, fez, garrison cap, hard hat, helm, helmet, high hat, homburg, hood, kepi (also képi), kufi, leghorn, miter (or mitre), nightcap, opera hat, overseas cap, panama, picture hat, pillbox, plug hat, porkpie hat, service cap, shako, silk hat, skimmer, skullcap, sombrero, sou'wester, Stetson, stocking cap, stovepipe, sunbonnet, tam, tam-o'-shanter, ten-gallon hat, top hat, topper, toque, tricorne (or tricorn), turban, zucchetto

warbonnet

eggheadedness, highbrowism, intellectualism

braininess, brilliance

acumen, alertness, apprehension, astuteness, discernment, discriminability, insight, judgment (or judgement), perception, percipience, perspicacity

common sense, horse sense, mother wit

aptitude, talent

sagacity, sapience, wisdom, wit

head, mind, skull