For reasons any competent psychologist must be able to explain, codes and ciphers in general seem to be inherently fascinating to almost everyone. When, in addition, they have to do with the most secret military messages of the Germans in World War II, the appeal is irresistible. Each new book about the British achievement of deciphering those radio signals, a triumph that played such an enormous role in helping defeat the Nazis, is welcome.

Peter Calvocoressi's slim volume provides the simplest, most sprightly and readily comprehensible account; the layman needs spend only a couple of hours with it to learn almost all he would care to know about the basic story, itself a secret until 1974.

To be sure, the book contains not a gret deal of new information (except for a splendidly lucid description of the form and workings of the Germans' then formidable enciphering machine, Enigma). The World War II buff will find more detail in Ronald Lewin's "Ultra Goes to War" and Patrick Beesly's "Very Special Intelligence," both admirable.

But Calvocoressi, who served throughout the war as an intelligence officer at Bletchley Park where Ultra (the British code name for the deciphered high-level German messages) was produced, brings a happy intimacy and fresh, first-hand rapture to his account. Restrained in all things but a passion for accuracy, he is punctilious in his assessments of where Ultra intelligence was crucial and where it was only of peripheral use.

He demonstrates, for example, how central and vital Ultra was to the winning of the war in the Atlantic against the U-boats (which otherwise might have brought Britain to defeat); how vastly important was the intelligence and reassurance it brought Allied commanders preparing for D-Day and in the following critical weeks; what significant role it played in the detection of the radio beam system that guided German night bombers (a story told in full in R. V. Jones' "The Wizard War"); how consequential it was to Montgomery's defeat of Rommel in Africa; how useful in so many other matters.

In the spring of 1941, the cryptographers at Bletchley solved "Red," the Luftwaffe cipher, and read it every day until the end of the war -- so successfully, in fact, that the intelligence analysts across the hall were inclined to be touchy if the message traffic, unscrambled on a machine whose settings were changed every night at midnight, were not decoded and ready for reading by breakfast.

Those messages were by far the most abundant and valuable, not in the form of spectacular and sudden disclosures of some top general's battle plans, but in thousands of tiny bits of less glamorous information: the supply of aviation fuel at some airfield, a squadron commander's report of his daily strength and readiness, a transfer of a unit from one base to another, a note on supply transport problems. Calvocoressi shows how it was the endless, often tedious and usually inspired piecing together of those endless fragments that permitted the British and American commanders to read the cards in the enemy's hand and to judge how they would be played.

It is easy to realize just how mind-boggling were the mathematical, engineering and cryptanalytical problems that were solved by Bletchley's code-crackers. "Top Secret Ultra" makes it clear that the processing of the decrypted material into the most abundant and coherent military intelligence ever available to any set of commanders in history was a task almost as demanding, and accomplished with equivalently awesome success.