Christine Lagarde, the head of the International Monetary Fund, has been found guilty of criminal charges linked to the misuse of public funds dating to her time as France’s finance minister.

She will not serve jail time or have to pay a fine. But her position at the Washington-based I.M.F. is on shaky ground, at a time when the organization faces questions over its participation in a multibillion-dollar bailout for Greece and uncertainty about the role of the United States in the organization. The fund’s executive board will meet later on Monday to consider its options.

Here is a quick primer on the case.

What was she charged with?

Ms. Lagarde was accused of “negligence by a person in a position of public authority,” related to a 2007 arbitration case involving Bernard Tapie, a French tycoon close to Nicolas Sarkozy, then France’s president. In the case, Mr. Tapie was awarded more than 400 million euros, or $430 million, to settle a dispute with the partly state-owned bank Crédit Lyonnais.

The size of the award stunned and angered the French public, and some of Ms. Lagarde’s advisers suggested that she take action to appeal the arbitration decision. But she declined to do because, her lawyer said, it would have resulted in costly new lawsuits by Mr. Tapie.