The books are (description stolen shamelessly from Wikipedia):
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The Coming of the Third Reich (1871-1933) (US ISBN 978-0713996487, 622 pages)
It describes the origins of the Nazi party, going back to the unification of Germany in 1871, and taking the timeline up to 1933, when Hitler and the Nazis completely seized power in Germany.
The Third Reich in Power (1933-1939) (US ISBN 978-1594200748, 960 pages)
It describes Nazi Germany during the so-called "peacetime" period, picking up where the first volume left off, and going all the way up to the start of World War II in 1939.
The Third Reich at War (1939-1945) (US ISBN 978-1594202063, 944 pages)
It describes the entire wartime period of Nazi Germany, picking up from 1939, where the previous volume ended, and taking the timeline to 1945 and the end of the war.
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TRaW focuses on "major turning points" in the war, namely:
The Conquest of Poland, 1939
The Conquest of France and the Low Countries, 1940
The Battle of Britain, 1940
The Battle of Moscow, 1941-42
The Battle of Stalingrad 1942-43
Beginning of the Combined Bomber Offensive - 1943
With a bit of filler in between them; for example, he covers the North African campaign(s) in a couple of paragraphs/pages; covers the early days of Barbarossa, etc etc.
From skimming the footnotes; you find that R.J. Evans relied much on a heavy trawl of secondary source materials in both English and German language, rather than relying on primary source documentation.
However, since much of the secondary sources are in German, it's not *that* bad; since to an English- only reader like me; those sources are inaccessible due to distance (would be primarily located in German libraries) and language (god I hope google books links in with google translate sometime soon).
Quite a bit of the information on Nazi War Production (or lack thereof) I recognize from the seminal The Wages of Destruction: The Making and Breaking of the Nazi Economy by Adam Tooze, which is referenced heavily in footnotes; and he relies heavily on Glantz for much of the Eastern Front fighting.
That said, the book is a very good survey of the Third Reich in power -- if you had only one book to recommend to a relative historical neophyte about why the Nazis (or their policies) were:
A.) Evil
B.) Everywhere
C.) Incompetent
D.) Had 0% chance of winning the war
this book would be a good one for that choice.
Unfortunately, since this relies on a trawl of secondary sources to generate a coherent narrative; some serious boo-boos creep in; like:
For example, in the photographic plates, under a photo of StuG IIIs in production, the label is Tiger Tanks in production, summer 1943.
It also briefly (in a few sentences/paragraphs) covers the bullshit claims made by Rainer Karlsch regarding a second German Bomb program and an alleged explosion in Thuringia.
What it does very well however, is lays out in a coherent narrative, the overall Nazi policies regarding conquered areas and territories, and the programs carried out within.
For example, there's a ton of quotable lines regarding this referneced in the book:
"He is not to hang partisans up 100 m in front of my window. Not a pretty sight in the morning."
-General der Infanterie Gotthardt Heinrici regarding executions carried out by his interpreter, Leutenant Beutelsbacher.
"Your mission, is to be carried out in a country in which in 1914 rivers of German blood flowed because of the treachery of the Serbs, men and women. You are the avengers of the dead. An intimidating example has to be created for the whole of Serbia, one that hits the whole population in the severest manner. Anyone who shows mercy is betraying the lives of his comrades. He will be called to responsibility without respect of his person and put before a court-martial."
-General Franz Friedrich Böhme on 25 Sept 1941 to his troops.
Böhme also laid out the ratio of 100 dead hostages for every dead German, and 50 dead hostages for every wounded German; leading to stuff like units of the 717th Infantriedivision shooting 300 men in the town of Kraljevo, then going on to round up 1,400~ further Serb hostages and shooting them to meet their quota.
For the Chetnik uprising, which killed 160 soldiers and wounded 278; Austro-German (many of the units in the Balkans were commanded by Austrians or filled with Austrians) troops shot about 20,000 and 30,000 Serbs.
I could go on and on like this, but the book goes on and on; hence my recommendation for this book as being a good one to give to someone to disabuse them of the myth of an apolitical German Army being mostly clean, while all the meanness and nastiness was done by those people in the SS.
The book also covers just how well the Holocaust or it's various offspring/offshoots were open secrets in Nazi Germany during the War years.
Atrocity tourism: German troops take snaps as an alleged partisan is hanged in a Belarussian town in January 1942.
Imagine that photo and the accompanying letter to the family back home multiplied by a lot -- along with a lot of other events; like when a Viennese soldier returned to his regiment in Belgrade from leave home; his comrades greeted him with "Are you going along with us to shoot Jews?"
It also covers the T4 'Aktion' program in some detail, which is important in helping understand why orders from Hitler and the higher Nazi echelons were incredibly vague, w.r.t. the Holocaust -- because of the backlash from the German Catholic/Protestant community once the T4 'Aktion' program became an open secret; so future programs like T4 were to be couched in the most vaguest terms, allowing just about anything to be read from them with enough massaging.
The "cleanup" programs for the Death Camps are also covered -- about how the Nazis sent groups to early killing field sites when possible to dig up the corpses from mass ditches and burn them; and also dug up ditches at death camps from the early years when things weren't as systematized for disposal.
They also planned the "cleanup" of the Death Camps; e.g. after their mission was done, they began to blow up and dynamite the gas chambers and then the crematoria -- after killing the last couple hundred of "Special Detachment" prisoners -- then dismantled the guard towers, barracks, searchlights, etc and bulldozed over the site to return it to a patch of parkland.
From what I've read from the book; this was not out of fear of what would happen if Germany lost the war; etc, but as a proactive measure to clean up any evidence of the Holocaust that could be used in the future to deny the regime it's legimitacy -- e.g. for a a regime which uses the way the Communists acted in x,y,z as justification for wiping them out -- it just wouldn't do to have evidence of the German State carrying out a program that makes the Communists look like pikers lying around. So they had to be cleaned up.
There is also one case of BioWar covered in the book that I did not know about, except it was by the Germans against the Italians after the Italian surrender.
Meanwhile, Allied troops continued to fight their way slowly up the peninsula. In their path lay the Pontine marshes, which Mussolini had drained at huge expense during the 1930s, converting them into farmland, settling them with 100,000 First World War veterans and their families, and building five new towns and eighteen villages on the site. The Germans determined to return them to their earlier state, to slow the Allied advance and at the same time wreak further revenge on the treacherous Italians. Not long after the Italian surrender, the area was visited by Erich Martini and Ernst Rodenwaldt, two medical specialists in malaria who worked at the Military Medical Academy in Berlin. Both men were backed by Himmler’s Ancestral Heritage research organization in the SS; Martini was on the advisory board of its research institute at Dachau. The two men directed the German army to turn off the pumps that kept the former marshes dry, so that by the end of the winter they were covered in water to a depth of 30 centimetres once more. Then, ignoring the appeals of Italian medical scientists, they put the pumps into reverse, drawing sea-water into the area, and destroyed the tidal gates keeping the sea out at high tide. On their orders German troops dynamited many of the pumps and carted off the rest to Germany, wrecked the equipment used to keep the drainage channels free of vegetation and mined the area around them, ensuring that the damage they caused would be long-lasting.
The purpose of these measures was above all to reintroduce malaria into the marshes, for Martini himself had discovered in 1931 that only one kind of mosquito could survive and breed equally well in salt, fresh or brackish water, namely anopheles labranchiae, the vector of malaria. As a result of the flooding, the freshwater species of mosquito in the Pontine marshes were destroyed; virtually all of the mosquitoes now breeding furiously in the 98,000 acres of flooded land were carriers of the disease, in contrast to the situation in 1940, when they were on the way to being eradicated. Just to make sure the disease took hold, Martini and Rodenwaldt’s team had all the available stocks of quinine, the drug used to combat it, confiscated and taken to a secret location in Tuscany, far away from the marshes. In order to minimize the number of eyewitnesses, the Germans had evacuated the entire population of the marshlands, allowing them back only when their work had been completed. With their homes flooded or destroyed, many had to sleep in the open, where they quickly fell victim to the vast swarms of anopheles mosquitoes now breeding in the clogged drainage canals and bomb-craters of the area. Officially registered cases of malaria spiralled from just over 1,200 in 1943 to nearly 55,000 the following year, and 43,000 in 1945: the true number in the area in 1944 was later reckoned to be nearly double the officially recorded figure.