Amnesty International, the Human Rights Story, by Jonathan Power. New York: McGraw-Hill Book Company. 125 pp. $9.95.

Amnesty International is the organization governments love to hate. Moscow calls it a leader among ''organizations which conduct anti-Soviet propaganda.'' The Brazilian government calls it an ''instrument of communist terrorism.'' But for thousands of ''prisoners of conscience'' it has often meant the difference between anonymous suffering through unjust imprisonment, and freedom.

Jonathan Power's book chronicles the achievements, failures, and inner workings of the British-based Amnesty International's first 20 years. The book makes clear that the key to Amnesty's successes lies in its political impartiality, carefully verified data, and a strict mandate. It only adopts the cases of prisoners who have neither used nor advocated violence. Amnesty members conduct letter-writing campaigns on behalf of prisoners in the hope that the ''glare of public opinion'' will shame officials into humane treatment.