If one book can be said to have played most prominently in the 1984 presidential election, this is it. Walter Mondale referred to it during his second debate with Ronald Reagan. Just about every politically active person critical of Mr. Reagan's record on arms control drew heavily on it. Prominent administration officials have found it necessary to rebut the book publicly. Reporters covering the subject for the obligatory campaign ''issues'' post-election articles find it a most helpful review of the past four years.
All of this is with good reason, for Strobe Talbott's ''Deadly Gambits'' is really a remarkable book. No matter what the reader's political proclivities, he will be impressed with the thoroughness of detail and especially the view from inside. This is a book as much about the making of presidential policy as about the policy itself.
Talbott's essential theme is that during its first four years the Reagan administration was ''paralyzed and polarized'' on arms control, with agencies and (more important) strong-willed officials trying to undermine each other's positions, status, and relative power in high-stakes ''bureaucratic warfare.''
The Soviet Union may have had its succession problems - three leaders in two years - but there were similar difficulties in Washington. In one term, the Reagan administration had two secretaries of state, two directors of the Arms Control and Disarmament Agency, and three national-security advisers.
Meanwhile, the President's chief goal (to use Churchill's phrase) was ''arm to parley,'' closing the now largely discredited ''window of vulnerability'' by building up the US strategic arsenal. But on the details of arms control, Talbott asserts, Reagan ''was to remain a detached, sometimes befuddled character.''
Controversial presidential statements about being able to recall some nuclear weapons and the heavy Soviet emphasis on land-based missiles have been much reported.
Strategic weaponry and doctrine are highly complex as well as subtle, and one at times can sympathize with Mr. Reagan's failure to grasp the important nuances that must be considered in proposing important changes in US arms control policy.
But few national issues are more important than nuclear war and how to avert it.
And the picture of a President unwilling or unable to understand fully what's going on within his administration - and take firm control - is a troubling one.
What Talbott finds is that the ''bureaucracy churned away furiously, bucking its disagreements upward to the White House.... The President then acted less as a decisionmaker in producing policy than as a rather reluctant and uninformed arbiter,'' the author continues. ''It was a process that produced constant squabbles, temporary truces, and permanent, institutionalized acrimony.''
This is strong stuff, and defenders of the President may want to believe that this critique comes largely from those who oppose him politically. But Talbott, in a highly commendable reporting job, has drawn much of his information from many of the most important actors themselves. Many details about private conversations and long quotations from key officials can only have come firsthand.
There is plenty of color here as well, like the picture of US chief negotiator Edward L. Rowny pulling out his harmonica at a birthday party for one of his secretaries and asking staff members to join in singing the ''arms control theme song'' ... ''I'm Forever Blowing Bubbles.'' Or the President beginning to doodle the head of a horse during a National Security Council meeting.
''Deadly Gambits'' is highly readable, and should be popular with those only mildly interested in arms control and politics as well as those who follow the subject professionally or as the most fascinating of spectator sports. It will, however, take some concentrated effort to keep straight the military and diplomatic complexities.
Talbott (Time magazine's diplomatic correspondent) wrote a thorough study of the strategic arms limitation talks leading to the 1979 US-Soviet agreement that failed to win US Senate ratification (''Endgame: The Inside Story of SALT II''). This book is its sequel. The reviewer looks forward to what will have to be the third in a fascinating series, and he wishes the same quality of reporting and analysis could be done from the Kremlin.