Meaning "building where plays are shown" is from 1570s in English. Transferred sense of "plays, writing, production, the stage" is from 1660s. Generic sense of "place of action" is from 1580s; especially "region where war is being fought" (1914). Spelling with -re arose late 17c. and prevailed in Britain after c. 1700 by French influence, but American English retained or revived the older spelling in -er.
"wonder-worker," 1715, from Medieval Latin thaumaturgus, from Greek thaumatourgos "wonder-working; conjurer," from thauma (genitive thaumatos) "wonder, astonishment; wondrous thing," literally "a thing to look at," from root of theater, + -ourgia "a working," from ergon "work" (from PIE root *werg- "to do").
1590s, "conception, mental scheme," from Late Latin theoria (Jerome), from Greek theōria "contemplation, speculation; a looking at, viewing; a sight, show, spectacle, things looked at," from theōrein "to consider, speculate, look at," from theōros "spectator," from thea "a view" (see theater) + horan "to see," which is possibly from PIE root *wer- (3) "to perceive."
Earlier in this sense was theorical (n.), late 15c. Sense of "principles or methods of a science or art" (rather than its practice) is first recorded 1610s (as in music theory, which is the science of musical composition, apart from practice or performance). Sense of "an intelligible explanation based on observation and reasoning" is from 1630s.