Eliger is the aut by which a fid is admitted to a chapter within his or her math. After Eliger, the fid "graduates" from being a trainee and becomes a full member of his or her respective order. The aut is usually celebrated within a few years of the age of twenty.
An entire class of fids (those collected at the same time), will normally undergo eliger within a few days of each other. In a concent with multiple orders, there is some degree of politicking and horsetrading between the heirarchs and the orders to determine which fids will join which orders. Eliger is presumably derived from the Spanish verb "elegir," meaining to elect or to choose.