by Louise Richardson.

Random House. 300 pages. $25.95.

 The cool, analytic tone of Louise Richardson’s What Terrorists Want is part of her message. As an academic — she is executive dean of the Radcliffe Institute for Advanced Study — Richardson has decades of terrorist studies behind her; long before 9/11, she had staked out terrorist stories as her “hobby.” It was personal: her Catholic schooling in Ireland included reverence for the martyrs of 1916. At Trinity College, her “passionate hatred of Britain” gradually yielded to a fascination with how people living side by side could entertain diametrically opposed versions of the same violent event.

In What Terrorists Want, Richardson appeals to reason. The book is divided neatly in two: “The Terrorists” includes a historical long view, starting with the Zealots, Jews who sought to inspire a mass uprising against the Romans. The reader is struck by a sense of historical déjÀ vu. Richardson’s definition of “terrorist” reflects her awareness that they are far from crazy or immoral. To wit: Terrorists use violence against noncombatants to send a message to a third party. That’s it.

From the historical background and the definition that follows, Richardson draws her most useful analytical tool, the answer to the question implied by the title. Then and now, terrorists want the “three Rs”: revenge, renown and reaction. With these tools, she explains away the mystery of suicidal terrorism.

In the second part, “The Counterterrorists,” she provides a survey of successful approaches to terrorists, in light of the three Rs, and draws conclusions about our own “war on terror.” Many insights about the current global troubles emerge. All successful approaches spring from the strategic recognition, however imperfect, of what terrorists want. One begins to feel a sense of calm. Richardson has given us the weapon of understanding.

But understanding one thing can bring doubt about other things. Richardson’s imperative to know the terrorists on their own terms — the three Rs understood in context — should shape the coming debate. But who will start by repudiating the rhetoric of “the war on terror”? Wouldn’t that be political suicide?

Terrorists are evil, and our war is God’s war. Rooted in the identity politics of the colonial past, this strain of apocalyptic thinking is profoundly American. Today it cripples us. That said, the argument of this book offers us the best, perhaps the only, hope we have to weaken terrorists and put them out of business. It is indispensable.