In one narrow sense, the final book in Professor Evans's magnificent trilogy is an anti-climax. We know who lost the Second World War. We know about Dunkirk, D-Day and Dresden. His first two volumes, on the coming of the Third Reich and its seizure not only of power but of the German psyche, seem more immediately relevant seven decades on than another account of the subsequent battles and bestialities. Yet, in an almost Wagnerian way, you need to see the madness complete; you need to watch Berlin burning, a pyre of malevolent dreams. This is the fire Hitler built. This, crucially, is the history of his Reich set in its own obsessive context. This is the end of the party.

But that was probably always going to be the case. Evans tells the 1944 joke of a naive young German looking at a globe of the world: huge green swaths for the Soviet Union, pink for the British empire, mauve for the US. 'And this blue spot?' he asks, fingering Germany. 'Oh! Does the Leader know how small it is?'

We're used to other pens portraying 1939-45 as a titanic battle for survival between evenly matched forces, an equal struggle we almost lost. It's far rarer to have the practical situation clinically analysed, to see how the Reich - in weaponry, manpower, strength and resilience - was always overmatched. Once surprise had banished inertia and Britain had avoided defeat in 1940, the Allies were virtually inevitable victors; and Hitler as military leader was a fantasist in thrall to his own illusions. World domination? 'Germany's economic resources were never adequate to turn these fantasies into reality, not even when the resources of a large part of Europe were added to them.' The dream could never have come true.

Never underestimate Germany's sheer paranoia, though; for attack was also the Third Reich's deluded, defensive way of vanquishing its enemies close by and within. There were the Poles - 'more animals than men, totally dull and formless', Hitler declared, but still commanding German-speakers in former German territories. 'If Poland had gone on ruling... (here) for a few more decades,' Hitler said, 'everything would have become lice-ridden and decayed.' So 'the sub-human people from the East' had to be routed, obliterated or (if possessing blood good enough to make them a 'leader class') turned into Germans.

There were Gypsies, Ukrainians, Czechs, the halt, the lame: all to be shipped away or shot. The SS cleared Polish asylums, made patients stand in line, then buried them - 2,000 in a few brutal weeks of 1939. And, of course, there were Jews; the Polish Jews of the Warsaw ghetto, then of Germany itself. 'The Jews have deserved the catastrophe they are experiencing today,' Hitler told Goebbels in 1942. 'As our enemies are annihilated, they will experience their own annihilation... We must accelerate this process with cold ruthlessness, and in so doing we are rendering an incalculable service to a human race tormented by Jewry for millennia.' That service charge in cold statistics: three million murdered in the camps, 1.3 million killed by the SS, 700,000 disposed of in mobile gas chambers, a million starved to death. Incalculable, unforgettable infamy.

Professor Evans is history's master of the Holocaust. He knows its macabre facts and figures; his Reich books demonstrate in chilling detail how German hatred and resentment for failure turned in on itself and millions of its own inhabitants; he does not spare civil servants or doctors or scientists, or simple pillars of German society - they knew what was happening, they shared the guilt. Worse, they saw it as part of their own war effort, defending Germany against the dark forces that had brought it down. Extermination was not some irrational spasm consuming a few lunatics in temporary power. It was deliberate and condoned, in its own surreal context.

Almost bemusingly, we are asked through these pages to set mundane politics alongside such insanity, to see Hitler the politician gritting his teeth over party critics, persuading as well as ordering, losing any residual awareness of reality as his Berlin bunker implodes - in short, to realise that the strutting 'Great Dictator' of Chaplin was also one of a team struggling for supremacy and survival. In one sense, this Germany was berserk; in another, its wheels of government had merely veered a little off line while the engine of seeming normality chugged along. Only when Allied bombing raids began to shatter its cities did Germany awake to the horrors it had unleashed upon itself. Only when it looked closer did it begin to see the emotional cripples it had brought to power.

Could it happen again, Evans asks. Could our cosy Euroworld slither back into the cesspits of human behaviour? Maybe not in any literal Nazi revival way (though Austria provides scant comfort these days). But the Third Reich also stands as a wider warning of what havoc 'racism, militarism and authoritarianism' can wreak. In that sense Hitler's war against humanity never loses its awful force. The evil men do can always cross borders with impunity. Richard J Evans, in his restrained but passionate way, has an apprehension of times past that should warn us about the day after tomorrow. He seems to stand inside the Third Reich as it self-destructs. He sees its deeds in all their ghastly perversion. He always strives magisterially to make us understand - and to sense the demons within ourselves.