Keegan's book joins other one-volume histories of the war, most notably B.H. Liddell Hart's, A.J.P. Taylor's and Martin Gilbert's just published, horrifying, elegiac ''The Second World War: A Complete History,'' which carefully tots up the ghastly numbers of the dead after each military occasion. The only real competitor with Keegan is Liddell Hart. But precise and responsible historian as he was, his mind was narrower than Keegan's, and his powers of empathy either feeble or not fully engaged. Keegan, a writer as well as a scholar and thinker, emerges a clear winner, and both scholarly and general readers will be grateful for this book...

He quite correctly concludes that if Allied skill and bravery played their part in winning the war, American industrial power had an even bigger role, manufacturing in the year 1944 alone nearly 100,000 planes. ''In the final enumeration of Hitler's mistakes,'' Keegan writes, ''his decision to contest the issue with the power of the American economy may well come to stand first.'' Likewise, Keegan's book, although certainly not the last one- volume history of the war, may well come to stand first.