Washington ? Just by raising his hand and taking the oath of office, President Obama made history Tuesday. But from his inaugural address to throngs who crowded the streets of Washington to the diversity of the faces in his White House reviewing stand, he signaled that his presidency probably will bring even more widespread changes to a nation confronted by problems of historic significance.

Rarely has a president come into office with the public in such a seemingly conflicted mood. Battered by the worst recession since the Great Depression, Americans are deeply pessimistic about the nation’s future and their own well-being. The war in Iraq has taxed public patience. The war in Afghanistan and conflict in the Middle East challenge the shrewdest of leaders.

Obama’s somber address — and exhortation to the country to pull together — fit the times in which they were delivered. “Today I say to you that the challenges we face are real,” he said. “They are serious and they are many. They will not be met easily or in a short span of time. But know this, America: They will be met.”

Yet at a time of such doubt and despair, and on a day when the stock market plummeted again, Obama’s inauguration showed another side to the nation’s current mood, that of hopefulness and a sense of confidence that has been invested in a young and relatively untested new president.

It was to both uncertainty and optimism that Obama directed his words from the Capitol’s West Front to a sea of faces along the Mall and to street corners, churches and living rooms throughout the country.

He said: “On this day, we gather because we have chosen hope over fear, unity of purpose over conflict and discord.”

History infused every aspect of the day, including the first African-American president, and a generational shift away from the baby boomers who have led the nation for the past two decades, to a leader not part of the tumult of the 1960s to the return of Democratic Party control of Congress and the White House.

Most clearly, Tuesday’s activities confirmed that Obama’s presidency will mark a sharp break from the presidency of George W. Bush. The new president did not hesitate to highlight their differences.

Obama spoke of a change of course in the Iraq war and of the false choice “between our safety and our ideals.” Those last words were aimed at the previous administration’s positions on civil liberties and harsh interrogation techniques. Most striking, given Bush’s unpopularity abroad, was Obama’s declaration to a world watching intently and eagerly that “we are ready to lead again.”

Still, perhaps mindful that during his campaign he faced doubts about his readiness to lead in a time of war, he was careful to balance his pledge to use both diplomacy and cooperation in dealing with the rest of the world with steely words of resolve. To those out to harm the country, he said: “Our spirit is stronger and cannot be broken. You cannot outlast us, and we will defeat you.”

The confluence of events and Obama’s politics suggest that his presidency could bring a more momentous shift — from an era of conservative governance to one in which Washington assumes a more central role in the life of the country.

It is far too early to know how much Obama’s presidency will result in a rollback of the conservative era or the beginning of a new progressive era. But his aspirations are among the largest of any president since Lyndon Johnson, and he seems undaunted by that fact.

“There are some who question the scale of our ambitions, who suggest that our system cannot tolerate too many big plans,” Obama said. “Their memories are short, for they have forgotten what this country has already done, what free men and women can achieve when imagination is joined to common purpose and necessity to courage.”