She demurred, still bruised by the hurtful things that had been said about her from his side during the campaign (most hurtful of all, the charge that husband Bill, who before Obama used jokingly to be called America's first black president, was a racist). Obama persisted. It didn't take long for Clinton to be tempted.

Clinton says she liked the idea of following in the footsteps of one of her political heroes, William Seward, another senator from New York who lost his party's presidential nomination and then faithfully served Abraham Lincoln, the man who had beaten him, helping to abolish slavery in the process. She also says she was tickled by parallels with the fictional world of , where the president-elect offers his defeated rival the job of secretary of state and refuses to take no for an answer. It's nice to know that even the people at the top have spotted how often life now imitates TV.

However, this can't be the whole story. Clinton leaves out any mention of political calculation, saying only that "when your president asks you to serve, you should say yes". But political calculation is what the Clintons do for breakfast, lunch and dinner. Clinton says she consulted her husband, and it's impossible to think they didn't discuss what it would do to her chances of having another crack at the top job. It might not have looked like the most promising route back.

She comes across as consistently hawkish, pushing Obama to take stronger action in Afghanistan, Libya and Syria, though more cautious than some of the excitable young people around him when it came to the Arab Spring (his aides, she says, "were swept up in the drama and idealism"; not her). She is able to explain her thinking in detail, making clear that military action always has to be accompanied by a commitment to social and economic reconstruction - not hard power or soft power but "smart power". The underlying message is that if Obama didn't always listen, more fool him.

For most of her tenure this political strategy worked brilliantly. As Obama's first term drew to an end, she was the most popular politician in the country, her poll ratings far higher than those of her boss, since she was untouched by the struggle to get his domestic programme through Congress.

Then came Benghazi. The attack on the US consulate on September 11, 2012, which claimed the lives of the US ambassador to Libya and three of his countrymen, is the stick Clinton's opponents now use to beat her with. She has been accused of complicity in the disaster (the inadequate security at the consulate is said to rest at her door) and of trying to cover it up afterwards.

Conspiracy theories about what really happened abound, although the likeliest explanation for any gaps in the official narrative is cock-up rather than conspiracy: in the heat of the moment, different government agencies spun the evidence to cover their backs. But that doesn't stop the anti-Clinton conspiracy theorists from having a field day.

In the US, the Benghazi chapter of this book is the one that has been most eagerly awaited. It is fair to say that Clinton doesn't give much away. At the same time, she doesn't give an inch. She stands on her dignity, insists she acted at all times on the best information she had, profoundly regrets what happened, takes full responsibility but refuses to get drawn into the naked politicisation of a human tragedy. It's not so much a non-denial denial as a piece of non-political politics.

Will it silence the critics? Of course not. They will see it as more evidence that she has something to hide. It gives a glimpse of what any future Clinton campaign for the presidency will be like: the Republicans will try to open up her past; she will try to shut it down.

For those reasons, this is a pretty buttoned-up book. But it is not unrevealing. Clinton gives some clear indications of her likes and dislikes.

She doesn't seem to have much time for David Cameron, whom she appears to find too smooth (she much prefers William Hague); she is warily respectful of Angela Merkel; she was almost charmed by Nicolas Sarkozy; she thinks of Vladimir Putin as a thug.

Her silences often speak volumes. She says next to nothing about Samantha Power, the leading Obama foreign policy adviser who once called her a "monster"; and she makes no mention at all of Anthony Weiner, the husband of her top aide, Huma Abedin, who humiliated them all with the tawdriest of sex scandals.

Clinton says nothing about the state of her health, though it was bad towards the end of her time in office and is likely to dominate speculation about her future. She insists on her sense of humour, which, as so often, is a clear sign she doesn't really have one. She lists the number of times she went on David Letterman's show to make "pantsuit jokes" (telling us the number - it was three - doesn't add to the sense of fun). She recounts the moment when she tried to lighten US-Russia relations by giving her Soviet counterpart a literal "reset button", though unfortunately the Russian word for "reset" was misspelt to mean "overcharged". She tells us she was tempted to send the official responsible to Siberia. Ho ho.

Above all, what comes through is Clinton's sheer persistence. This is how she does politics, by keeping going and totting up the small victories so that they outweigh the defeats. Unlike Obama, who still appears to believe that politics is about rational argument, and unlike the elder George Bush, who thought it was about vision, Clinton believes it is about breaking things down. She is a disaggregator, who can't see a problem without trying to make it smaller, more manageable, and only then does she try to fit the pieces back together again. Peace, she tells us, doesn't necessarily begin with a grand fanfare. Sometimes it comes out of the temporary ceasefire that holds just long enough to make a difference.

Part of why this book is so exhausting is its thoroughness: she travels the world and tells us about the different challenges she faced, taking them all seriously. Early on she quotes approvingly a maxim from Deng Xiaoping: "Coolly observe, calmly deal with things, hold your position, hide your capacities, bide your time, accomplish things where possible." The US could do worse than having Deng as its next president.

is a prosaic book, but still, it is an amazing story. Think back to the first time Clinton entered the world's consciousness, in early 1992, sitting on a sofa for a joint TV interview to try to rescue her husband from the terminal damage Gennifer Flowers seemed likely to do to his presidential ambitions. It would have been barely credible back then that both of them might one day be president. But there was a true steeliness to that joint performance which gave a glimpse of the future. Their eyes told a story: we are not going away; we can keep going with this; we will outlast anything you have got.

Doggedness is not the only political virtue and it's not the most attractive one. But who's to say it's not the most important.