To give a lecture or speak before an audience; to read aloud or deliver an address (often used in formal/written contexts).
教授は来週のセミナーで日本中世文学について講ずる予定だ。
The professor is scheduled to lecture on medieval Japanese literature at next week's seminar.
式典で代表が感謝の言葉を講ずる場面があった。
At the ceremony there was a moment when the representative delivered words of thanks.
To devise and implement measures, strategies, or policies in response to a problem or situation (formal, often used in legal/administrative contexts).
政府は経済混乱に対して緊急措置を講ずることを表明した。
The government announced it would take emergency measures in response to the economic turmoil.
企業は情報漏えいを防ぐための対策を講ずる必要がある。
The company needs to adopt measures to prevent information leaks.
To reconcile with someone or bring about a settlement; to make peace or mend a relationship (somewhat literary/formal).
両社は長年の紛争について協議し、妥協案を講ずることで合意した。
The two companies negotiated their long-standing dispute and agreed to adopt a compromise plan.
彼は旧友と和解を講ずるために直接会って謝った。
He met his old friend in person and apologized in an effort to reconcile.
To recite poetry at a poetry gathering; to declaim poems (an archaic/literary usage referring to performing or reciting verse).
俳句会で彼は自作の句を講ずると、会場から大きな拍手が起きた。
When he recited his own haiku at the haiku meeting, the audience gave him a big round of applause.