early 14c., moustren, "to display, reveal, to show or demonstrate" (senses now obsolete), also "to appear, be present," from Old French mostrer "appear, show, reveal," also in a military sense (10c., Modern French montrer), from Latin monstrare "to show," from monstrum "omen, sign" (see monster).
The transitive meaning "to collect, assemble, bring together in a group or body," especially for military service or inspection, is from early 15c. The intransitive sense of "assemble, meet in one place," of military forces, is from mid-15c. The figurative use "summon, gather up" (of qualities, etc.) is from 1580s.
To muster in (transitive) "receive as recruits" is by 1837; to muster out "gather to be discharged from military service" is by 1834, American English. To muster up in the figurative and transferred sense of "gather, summon, marshal" is from 1620s. Related: Mustered; mustering.
late 14c., moustre, "action of showing, demonstration, manifestation, exhibition" (a sense now obsolete), from Old French mostre "illustration, proof; examination, inspection" (13c., Modern French montre), literally "that which is shown," from mostrer "appear, show, reveal" (see muster (v.)). Meaning "an assembly or act of gathering troops" is from c. 1400. Meaning "a register or roll of troops mustered" is from 1560s. To pass muster "undergo review without censure" is by 1620s; in the form pass the musters it is attested from 1570s.