It is 25 years since the Berlin Wall fell and a new Germany was born. In the last quarter of a century the country has seen an unprecedented opening up of archives and a programme of national education and much public debate about the different inheritances of East and West Germany. There has also been an unprecedented building of monuments marking the horrors of the recent past. But what are the memories that German citizens bring to their new state? What, in short, does the world look like if you are German?

At the forefront of that memory is the Third Reich and the Holocaust.

But there is more than that, and one of the ways that German history is not like other European histories is that Germans consciously use it as a warning to act differently in the future. As the historian Michael Stürmer says, "for a long time in Germany, history was what must not be allowed to happen again". This is very different from Britain or France, where most public engagement with history, in terms of monuments and memorials, is to honour valour and heroism, with little public recognition of any wrongdoing, or of follies that might have led to the wars in which the valour had to be demonstrated. What is striking about German war memorials is that they look forward not back – a characteristic clearly visible in their parliament building.

The historic Reichstag was burnt out in 1933, with the fire blamed on the communists and used to advantage by the Nazis. During the war it was badly damaged, then occupied by the Russians. After reunification the decision was made to restore it, but the marks of the 1933 fire, as well as graffiti made by Soviet soldiers, were left untouched, as a reminder to legislators that if you get things as wrong as Germany did then the consequences are unimaginably terrible. An MP travelling to the Reichstag today will pass not only the Holocaust memorial but also memorials to the killing of homosexuals, disabled people and Roma. When they get to the building, they find it topped by a huge glass dome, to which the public have access. So not only do you have an emblem of a transparent legislature, but the public can literally exercise oversight over their government – a direct reversal of the situation under both the Nazis and the Stasi.

In effect the building is a meditation on different aspects of history. I can't think of another country in the world that lives so closely with the acutely uncomfortable reminders of its past in order to help it act more wisely in future.

In making our radio series, British Museum exhibition and book we have tried to look at objects that evoke memories of which pretty well all Germans can say "this is part of me". Some are obvious, such as the Gutenberg Bible. Every German knows that Germany invented printing and, in that sense, made the modern world. But we have also tried to focus on elements that the British public might not be so familiar with, as well as areas of German history about which there is still a reticence in Germany. People talk about the Holocaust very honestly and fully, but subjects such as the huge civilian losses from allied bombing raids are little discussed, unlike in this country. Yet it remains a potent memory.

It has always been the British Museum's job to present the history we need in order to make sense of now. Germany is the European state we most need to understand if we are going to comprehend both Europe, and the world.

Taucheranzug (Wetsuit)

'An instrument of state surveillance'

The wetsuit used in a failed escape attempt from East Germany. Photograph: Richard Ansett/BBC

The official account of oppression in East Germany does exist in the state archives, but it is written in such a deliberately bland and concealing way as to give very little impression of what actually happened. This cheaply made blue wetsuit with white zips, probably worn only once, tells you far more. Breaching the Berlin Wall wasn't the only route to the west. A hundred miles north was another favoured crossing point, if you were willing to sail across the Baltic in a rubber dinghy, as the owner of the wetsuit had intended to in November 1987 – despite the likeliest outcome being either dying of hypothermia or being shot. In this instance, the man was arrested before he even set off, but the fact was that people were still willing to risk their lives just two years before the Berlin Wall came down. Equally revealing is what happened after the man was sent to prison and the wet suit was confiscated by the Stasi. They used it as a training prop to instruct their informants as to what sort of products they should watch out for. Why would anyone need a wetsuit, or plastics or rubber that could be made into a wetsuit, or a dinghy, or anything that could be turned into a flying machine, or used as tunnelling equipment? And so on. If you saw your neighbours buying, or possessing these things, you were to let the Stasi know. So the wetsuit is not only evidence of one citizen wanting to flee, it also became an symbol of state surveillance, designed to prevent others from trying to escape.

One of the most remarkable things to come out of opening the Stasi archives was evidence of the extent of this surveillance. It is reckoned that one in three of the population of the GDR was at some time, in some way, informing on their friends, neighbours or families. The memory of that has had profound implications for the new German state. If you walk round Berlin today you will see – in stark contrast to Britain – almost no CCTV cameras. Edward Snowden's revelations of state surveillance made him, again in contrast to the UK, something of a national hero in Germany, with effigies of him paraded in the streets during Mardi Gras carnival processions. Germany's assiduous public study of its uncomfortable modern history has ensured that every adult knows what happened under both the Nazis and the Stasi. They know these things were done by the state in the name of the people. This wetsuit is a reminder of what can happen if the citizen fails to keep the state under control.

Tischbein's Goethe

'A citizen of the world'

Tischbein’s Goethe in the Roman Campagna (1787). Photograph: U Edelmann/Städel Museum/Artothek

We tend to think that all the great writers are somehow the same: Dante, Shakespeare, Cervantes. But Goethe is different. Of course, he is the great writer that every German schoolchild learns and reads as we do Shakespeare, but more than that he represents a German belief in openness to the world. The 1787 Tischbein portrait is the most famous portrait in the whole of Germany. It shows Goethe in Italy. He had just become a European celebrity after the publication of The Sorrows of Young Werther (the Clockwork Orange of the 18th century), and he was the first to make German a literary language read by foreigners. There is a wonderful German word – Weltbürger – a citizen of the world. That is how Goethe is shown here. Engaged with, appropriating and interpreting the whole world, he makes clear that you need to know about Britain and France, about Greece and Rome – you cannot have a culture that is only German. He also, strikingly, engaged with Islam in a way that is a significant part of the contemporary debate about how Germany should respond to its Muslim population.

Understandably, the Nazis were ambivalent about him. He was, of course, a hero, but they didn't like the indecisiveness of his protagonists (most of his heroes can't make up their minds), and, above all, they didn't like his willingness to look for models of behaviour outside Germany.

Würstchen

'A memory of their local sausage'

Photograph: Getty

De Gaulle once complained about how difficult it was to govern a country with 246 different cheeses. He did not know how lucky he was. Germany has more than four times as many types of sausage. What those sausages tell you is that the regional identity of Germany is still flourishing in a way that has probably never been the case in England, where there has been a centralised government in a dominant London for 1,000 years. Because of Germany's political fragmentation until 1870, and the deep differences in dialect and local history, there is a lively regional variety in Germany, expressed gastronomically through wine, beer and sausages, and politically through the Länder system. Each Land, or state has its own two-house parliament. Hamburg, for example, has survived unbroken as a city state since the early Middle Ages.

One of the big questions for a country that has never had fixed frontiers at its edges, and contains an extraordinary range of diversity, is: what does it share? Language, beer and sausages are among the shared things, and all have pronounced local flavours. Even today you can tell where you are in Germany by what kind of sausage you are offered and the way people – of every class – pronounce their German. Pretty well all Germans carry both a local accent, and a memory of their local sausage.

Dürer

'National artist of Germany'

Detail from Dürer’s Knight, Death and the Devil (1513).

Within a generation of the invention of printing, the Germans had done everything you can do with print; books, broadsheets, pamphlets and images. The great concentration of autonomous cities linked by rivers in south Germany provided the ideal communications and distribution network for a large, literate and prosperous population. Albrecht Dürer, working in one of the great trading centres, Nuremberg, realised that as a maker of prints he could sell his art across the whole of the continent, and, just as Goethe was the first German writer to be read across Europe, Dürer was the first major artist anywhere to make his work for a pan-European market. To protect his continent-wide success, he invented his own logo, in the form of the famous AD (which he later successfully defended in Venice). His work is familiar to every German, in particular his two great engravings, Knight, Death and the Devil, and Melancholia, which were long taken as two aspects of one national self-portrait: the knight riding bravely out to do what must be done; the figure of creative genius slumped on the floor, aware of so many creative possibilities that he is unable to act at all. The different sides of the German spirit.

Dürer is a national artist of Germany in a different way from Turner or Constable in Britain, who explore landscape. Dürer, working in the early 16th century, is focused on character; you may explore your own – and Germany's – experiences in the light of his images.

Meissen

'The celebrated porcelain menagerie'

Dürer’s Porcelain Rhinoceros (1515).

All Germans know their country is one of the great centres of technological innovation. And one of the great technological breakthroughs ever was made by Johann Böttger, a man who was something between an alchemist and a chemist working in Dresden in around 1710. He was the first European to discover how to make porcelain. At the time, Chinese porcelain was one of the most precious things in Europe, but nobody in the west knew what it was made of. After a long process of trial and error, Böttger worked it out. The result was that his patron, Augustus the Strong, ruler of Saxony, now had something that no other European head of state had, or could give as a present to potential allies. For a few decades Dresden porcelain was Saxony's equivalent of panda diplomacy.

The Chinese had used porcelain in quite limited ways, for vessels and dishes. Dresden flamboyantly made sculptures, especially of animals, demonstrating total mastery of a very difficult medium and technique. In the celebrated porcelain menagerie in the royal palace, the figures of the hen, fox, peacock etc were modelled on real animals. But for the rhinoceros the craftsmen went to Dürer, who had never seen a rhinoceros, but nonetheless produced a print based on reports sent from Lisbon. By the early 1700s, real rhinoceroses had been seen, but, like many Germans before and since, they preferred to see the world through Dürer's eyes. The Dresden porcelain rhinoceros, with its pugnacious charm and its anatomical oddities, is completely unforgettable.

After the second world war, Meissen found itself in the Soviet zone, but the Russians kept the industry going, and so the factory set up by Augustus the Strong received commissions to make official portraits of the leaders of the communist East German state. You can't be a ruler of Germany, control Dresden, and not mind about porcelain.

Volkswagen

'Supremacy in precision engineering in metal'

The Germans are masters of metal. In the Saarland and the Ruhr there is a metallurgic tradition that goes back thousands of years, and the country has long defined itself through high-end metal engineering in every field. By 1500, precision instrument making was dominated by south Germany and that is where buyers still go today. Gutenberg could make movable type only because there were people nearby who knew how to manufacture hundreds of identical pieces of metal. Shakespeare talks about expensive German clocks. Despite what Harry Lime, the third man, said, it was Germany not Switzerland that almost certainly invented the cuckoo clock.

Unsurprisingly, the Germans were also the first people to dominate the top end of the car market with Daimler-Benz and Mercedes. But one of the extraordinary developments of the 1930s was that Hitler decided he wanted Germany to be like the US and produce cars for everybody. The Volkswagen was an attempt to do something odd in German history, produce a low-cost, mass-market engineering product. But it was not an economic proposition, war was approaching, metal was needed for other things, and production was stopped.

After the war the British took over the plant, but no British car manufacturer liked the design and so the Germans resumed ownership. Reverting to their high-skill traditions, they then turned what had been meant to be a cheap mass‑market car into something of extremely high quality, but with as low a price as possible. The Volkswagen became the emblem of both the long German tradition of supremacy in precision engineering in metal, and also of the postwar economic miracle of the Federal Republic.

Kollwitz

'The grief of the survivor'

Käthe Kollwitz’s Pietá (1937).

In Britain, France and elsewhere, most war memorials are designed to honour the dead. What is striking in Germany is the focus on those who are left; monuments that depict the grief of the survivor. And in the 20th century, with its many catastrophic killings, there have been many grieving survivors. Käthe Kollwitz explored all through her life how the image of one mother's pain can carry the sorrow of a continent.

Kollwitz was a mother whose son had died in October 1914. Peter had been too young to join up for the first world war and needed his father's approval. The father was reluctant, but Kollwitz persuaded her husband to let the boy go. He was killed 10 days later. So she had not only a profound sense of loss, but also of guilt and responsibility. When she was asked to provide the memorial at the cemetery where her son was buried, she turned that mix of emotions into an exploration of the cosmic tragedy of the first world war. She made a simple image of two parents, on their knees, separate, isolated in their own grief, looking over the cemetery full of the young dead. There is no image of the son.

In 1937, Kollwitz was still working through the sorrow of 1914 and on the anniversary of her son's death that year she wrote in her diary about making a small sculpture that has "become something like a Pietà [a depiction of Mary with the dead Christ]". But she had moved far away from any Christian tradition or convention and found a powerful way of articulating the desolation of those who are left. Nothing in this later sculpture suggests sacrifice to achieve a higher purpose. There is no hint of salvation, merely a silent response to slaughter.

After the reunification of Germany in 1990, Chancellor Helmut Kohl proposed a National Monument to all Victims of War and Tyranny in the Neue Wache in Berlin. The image he chose was an enlarged version of that sculpture created in 1937 by Kollwitz, herself both witness and victim. It was a striking, brilliant insight on the part of Kohl to see the analogy between Kollwitz's mother protecting her child, and the state's recognition of its duty to defend all those over whom it has power – and in either case, the terrible cost of failure.

Buchenwald

'A quiet, profound protest'

Buchenwald Gate. Photograph: Corbis

All the concentration camps had slogans on their gates. Often it was Arbeit Macht Frei (Work makes you free). However, in Buchenwald, a labour (not a death) camp – although many thousands of people were worked to death or deliberately killed there – the Nazis chose the motto Jedem Das Seine (To Each What They Are Due). It was placed on the inside of the gate rather than the outside, so that every prisoner was reminded of it as they looked to the world outside.

The words are a powerful statement – and in this context a complete and provocative perversion of any notion of justice. They are the German translation of the Roman law maxim Suum cuique, incorporated not just into German law but legal systems across Europe. They are the title of a Bach cantata performed in Weimar, the city of Goethe and Schiller, just 10 miles from Buchenwald. And this gate, so close to Weimar, raises the unanswerable question of modern German history: how can these different components of the German story fit together? How could all these humane traditions of justice and scholarship, music and law – of a civilised society – all collapse in the Nazi abyss?

The Nazi authorities conscripted one of the inmates of the camp to design the words. Franz Ehrlich had been interned as a communist on trumped-up charges of treason. He had trained at the Bauhaus, the famous school of design, also in nearby Weimar, which was loathed by the Nazis for its internationalism and modernism. Ehrlich nonetheless used a beautiful Bauhaus typeface of the sort that the Nazis categorically disapproved of. Astonishingly, they didn't seem to notice. It is impossible not to read the sign as a quiet, profound protest. Ehrlich was compelled to design this hateful, callous motto, but he did it in a way that showed that another Germany, a humane, international Germany, survived. These shocking words in that typeface suggest that people, even in terrible circumstance, may sometimes find a way of asserting dignity.

Trümmerfrauen

'The rubble women'

Lachnit’s Trümmerfrau (1945-46).

WG Sebald has written about the striking gap in German public and literary discourse about what the allied bombings did to the civilian population. There is probably more debate about the fire-bombing of Dresden in this country than in Germany. Sebald suggests this may be because the bombing was seen as deserved retribution and therefore the victims were not entitled to talk about their suffering. But the memory of the bombings and the losses is strong, and Dresden is a very particular case and memory. The same Augustus of the porcelain rhinoceros also built the beautiful 18th-century city and filled it with supreme art treasures . Then, on the 12th and 13th ofFebruary 1945, the city was, reduced to rubble by British and American bombers. Later In July and August that year the Soviets removed the entire art collection. Every part of Dresden's identity had been lost. But how did you start clearing up the colossal mess? All able-bodied women – there were few men – were conscripted to clear the rubble, mostly with their bare hands. And with astonishing speed the Trümmerfrauen (the rubble women) made Dresden, and Germany, habitable again by clearing away not only the destroyed buildings, but also the thousands of bodies that had been incinerated within them.

The sculptor Max Lachnit, who worked in Dresden, lost all his work in the air raid. He made this little statue of one of the Trümmerfrau from bits of coloured stone he found in the ruins. She is young, looking steadfastly forward, totally impassive. We have no idea who she is – she stands for thousands. It is not a great work of art, but it encapsulates one of the deep memories of many Germans, of the endless rubble, of the late 1940s, and of the huge army of women who cleared it. Only then could the reconstruction of the cities, and the economy, begin.

Barlach's Angel

'The quest for resolution and reconciliation'

Barlach’s Angel (1927).

The biography of Ernst Barlach's sculpture is the biography of Germany in the 20th century. Barlach had joined up for the first world war as a committed patriot who wanted to fight. His experience of the trenches had made him a pacifist. He built this memorial to those killed in the war and to remember those who remained – using the face of his friend the artist Käthe Kollwitz – for the Protestant cathedral of Güstrow, a small town just over 100 miles to the north of Berlin. His Hovering Angel, suspended from the ceiling – so elevating individual grief into general mourning – is an evocation of a mother looking west, to the killing fields of Flanders, grieving serenely, perpetually, for her dead son. It is about reflecting on responsibility for the war, and sorrow for its consequences.

Of course, the Nazis hated its pacifism. Eventually they took it away and melted down the bronze to use as material for the next war. After it was removed from the cathedral in 1938, Barlach's friends, assisted by a dealer who had suspiciously good relations with the authorities, located the original plaster mould and made a second bronze, which was buried for safe-keeping. When that emerged after the war, it was in the west, and the angel's previous home Güstrow, a small town just over 100 miles to the north of Berlin was in the east. So the second bronze went to the Antonite Church in Cologne. There, on the slab in the floor below it, they added to the dates 1914–1918, the years 1933-1945. The strength of the Angel's symbolic power, they believed, was able to carry not just the sorrow of the first war, but the added burden of the further millions of losses and deaths of the entire Nazi period.

In the early 50s, against the backdrop of the cold war, another cast of the version in Cologne was made, and sent to Güstrow, as an act of reconciliation and friendship. So another layer of meaning was added to Barlach's image. When in 1981 West German Chancellor Helmut Schmidt made an official visit to East Germany, he stood beneath the angel in Güstrow with GDR leader, Erich Honecker and talked of what the two German states might share. When we asked to borrow it for the British Museum exhibition, the congregation of Güstrow Cathedral had to give their agreement. After much reflection they eventually decided that the purpose of the object was to promote healing and reconciliation, and that, 100 years after 1914, reconciliation was still needed between Britain and Germany. So it will come to London. In the exhibition here, this third version of Barlach's Angel will embody the war fever of 1914; pacifism in the 1920s; the humane art of Käthe Kollwitz; the destruction of "degenerate art" by the Nazis; the western front in the first world war and the bombing of Berlin in the second; the postwar division of Germany and the dialogues that were possible in spite of it; the millions of victims of 20th-century conflicts; the continuing painful and difficult conversations between Germany and the rest of the world in the quest for resolution and reconciliation; and unquenchable hope.

I can't think of any other exhibit that has such profound resonance. I hope people will respond to the generosity and earnestness of the people of Güstrow, who, by allowing it to come to London, have added yet another new dimension to this remarkable sculpture.

• Germany: Memories of a Nation is on BBC Radio 4, Monday to Friday at 9.45am, for six weeks from 29 September. The exhibition opens at the British Museum on 16 October, britishmuseum.org. Germany: Memories of a Nation by Neil MacGregor is published by Allen Lane on 6 November (£25).