The 20th century is littered with the febrile architectural dreams of megalomaniacs: Mussolini's modernist recreation of imperial Rome, Saddam Hussein's Mother of all Battles mosque and the Arc of Triumph, the monumental kitsch of Kim Jong-Il's horrific Ryugyong hotel to name but a few. But there are none more deranged than Adolf Hitler and Albert Speer's vision of Germania. Hitler wanted to tear down Berlin to rebuild his world capital, poring over the architectural plans for hours on end. Chillingly, Speer wanted to make sure the buildings would also make great ruins. The realisation of Germania would have made Haussmann's reconfiguration of Paris seem cosmetic.

At the end of Albert Speer, the David Edgar play based on Gitta Sereny's Albert Speer: His Battle with Truth, Speer says: "The BBC never fails to delight in the irony that all that remains of my vision for Germania are the ruins of a stadium, two lavatories and some street lamps." Thankfully, the allied bombers got there before the Nazis could begin building their 1,000-year capital.

The plans for the Great Hall (Volkshalle) were kept from the public until 1943, though Hitler hinted at its size when he said in 1938 that Berlin Cathedral, which had seating for 2,450 people, "should hold 100,000 people ... we must build ... as big as today's technical possibilities permit, and above all we must build for eternity!" It would have been the largest enclosed space in the world, holding up to 180,000 people – there were worries that the exhaled breath of the audience could create its own precipitation. This inhuman scale only made sense in terms of Berlin being made a global capital. Inspired by the Pantheon in Rome (and especially its oculus), it was essentially a temple to Hitler.

It's a shame that the photograph of the model showing Speer's plans for the creation of a north-south axis for Berlin in the endpapers have the 7km-long, 120m-wide central thoroughfare and Triumphal Arch obscured by the fold of the book, for this is the very centre of Germania. The arch in front of the new South Station was to be dedicated to the German dead from the first world war and, writes Friedrich, "It made sense that the Great Hall marking the northern boundary of the north-south axis should ensure that Hitler's rewriting of history should find its architectural counterpart in a quasi-religious edifice celebrating the victory of the troops of the 'pan-German Reich' in the coming world war under Hitler's supreme command."

If Berlin is indeed the abused city of the title, then Friedrich has written a kind of autopsy report, a brilliant examination of the way Hitler used the city, treating it as a "lab rat on which he could try out his architectural experiments and ideas on urban planning". Hitler's Berlin is a comprehensive account of the rise of the National Socialism that details precisely how it emerged from within the city itself rather than being imposed from outside, and how Joseph Goebbels as the Gauleiter used violence, propaganda (especially in his newspaper, Der Angriff) and the incitement and blame of the communists to further its reach.

Friedrich argues that scholars have read too much into a handful of quotations from Mein Kampf that suggest Hitler "never liked Berlin" and was forced against his will to leave Munich. He challenges the biographer Joachim Fest's view of Hitler that he "despised its greed and frivolity … he stood baffled and alienated by the phenomenon of the big city, lost in so much noise, turbulence, and miscegenation". Hitler hated the Weimar decadence, and no doubt the lack of party-political success he had there played its part, but what, asks Friedrich, of his visits to Luna-Park; his praise for the Tiller Girls, his cinema-going and enthusiasm for cars? Is this a man terrified of the urban jungle? Rather, Friedrich argues, Hitler had an "instrumental relationship" to Berlin, first regarding it as "wonderful" in its "visible power and grandeur", but ultimately as a place where "antisemitic attacks could be staged, Nazi rituals could be rehearsed and the conquest of the public arena could be planned in detail".

Friedrich quotes from postcards Hitler sent from Berlin to his friend Eric Schmidt in his 20s and articles he wrote, to paint an intriguing and detailed picture of how his conception of Berlin evolved. When he was younger, Hitler saw himself working as an architect there, "fascinated first and foremost by the buildings", especially of the neo-baroque and neo-classical type. At a meeting in 1933 he announced that Unter den Linden, the palace and their immediate vicinity were "the only monumental buildings", marking "the high point of the city both culturally and in terms of its urban design", having earlier railed against "a thousand superficial impressions – cheap neon advertising, sham politics everywhere you look".

Perhaps the most disturbing monument to Germania and Hitler's plans is a huge circular concrete block weighing more than 12,000 tonnes in the Tempelhof district – the Schwerbelastungskörper – that was put there to test whether the sandy soil could take the vast weight of the proposed Arch of Triumph. Friedrich writes with weary pathos that this "massive and mysterious concrete building … continues to weigh figuratively on Berlin ... a symbol of the way in which the city remains oppressed by Hitler's legacy"