Nonfiction briefly . . .; Miller's Court, by Arthur R. Miller. Boston: Houghton Mifflin Company. 302 pp.

Arthur Miller, the Harvard law professor, is known to many television viewers through his show, ''Miller's Court,'' a sort of Socratic discussion of controversial issues involving the law. His book by the same name has virtually the same format. Dealing with such subjects as school prayer, free speech and civil disobedience, sports violence, landlords and tenants, and genetic engineering, Miller explains, questions, and prods - inviting, as much as is possible, a dialogue with his readers.

The subjects, he admits, have been chosen ''for their dramatic and emotional appeal, contemporary relevance, and their value in illustrating various aspects of the legal process.'' By no means an exhaustive treatment of each topic, the book, he says, is intended to help readers understand ''how the legal process works, why it operates the way it does, and ultimately to allow you to form your own judgment as to whether it's really as gummed up as cynics claim it is.''

Miller succeeds in doing just that. One can't help but think about the issues he raises. That in itself makes ''Miller's Court'' worth reading. Randy Shipp