President Reagan accepted the nomination of the Republican Party for a second term tonight with the claim that his administration has brought "a springtime of hope for America."

"Greatness lies ahead of us" if he is reelected, Reagan said as he called upon voters "to renew the mandate of 1980, to move us forward on the road we presently travel . . . , the road leading to prosperity and economic expansion in a world at peace."

In a speech aimed as much at undecided voters watching on television as at cheering Republicans in the Dallas Convention Center, Reagan declared that "America is presented with the clearest political choice of half a century."

"The choices this year are not just between two different personalities or between two political parties," Reagan said. "They are between two different visions of the future, two fundamentally different ways of governing -- their government of pessimism, fear and limits and ours of hope, confidence and growth."

Focusing more on what he said he had accomplished in the last four years than on details of what he would do if he wins a second term, Reagan contended that he had kept promises to achieve economic recovery and "restore our ability to protect our freedom on land, sea and in the air."

Speaking before a loudly responsive audience, Reagan proclaimed that, under his presidency, "not one inch of soil has fallen to the communists," which provoked the first of several chants of "Four more years." He then suggested that Democratic presidents who preceded Jimmy Carter would have taken similar pride in such an accomplishment.

The United States, Reagan said, demonstrated its resolve in the cause of freedom by rescuing American students on the "imprisoned island of Grenada."

"Democratic candidates have suggested that this could be likened to the Soviet invasion of Afghanistan, the crushing of human rights in Poland or the genocide in Cambodia," Reagan said. "Could you imagine Harry Truman, John Kennedy, Hubert Humphrey or Scoop Jackson making such a shocking comparison?"

"No," the crowd roared.

His speech provided the climax to a Republican convention marked until tonight by the conservative rhetoric of its platform and an absence of drama. After waiting all week for Reagan to arrive in the hall, delegates gave him a tumultous welcome. Vice President Bush had warmed up the crowd with a denunciation of the Democratic ticket, and Reagan was introduced with a nostalgic film, which he narrated, extolling the record of his presidency.

After his speech, the convention closed in a shower of balloons as Nancy Reagan, Bush and his wife, Barbara, clustered around the president, and Ray Charles sang "America the Beautiful." Then delegates joined hands and sang "God Bless America."

Reagan's speech was designed to rekindle some of the optimism that pervaded the 1980 Republican National Convention in Detroit and has been a trademark of his presidency. It also was intended to mollify moderate Republicans, independents and city-dwellers who may have felt slighted by what critics have called the narrow, conservative focus of the GOP platform.

Tracing the journey of the Olympic torch across America, Reagan told stories of spontaneous displays of patriotic singing and of a scene in San Francisco where a Vietnamese immigrant, "his little son held on his shoulders, dodged photographers and policemen to cheer a 19-year-old black man pushing an 88-year-old white woman in a wheelchair as she carried the torch.

"My friends, that's America," Reagan said.

In an emotional peroration, Reagan said the Olympic torch and the games that followed it in Los Angeles this summer symbolized the "melting pot" of America. It was also reminiscent, he said, of the torch on the Statue of Liberty, which he said held out the "glistening hope" that "every promise, every opportunity is still golden in our land."

Much of Reagan's speech, however, focused not on opportunities for America but on what he depicted as the "decline" that he said afflicted the nation before he became president and that he contended would return if Democratic presidential nominee Walter F. Mondale wins the election Nov. 6.

Reagan contended that "the position of poor Americans worsened under the leadership of our opponents" and said the largest annual increase in numbers of persons living in poverty took place between 1978 and 1981.

Those statistics ignored recent reports showing that the number of Americans in poverty has increased during his administration and that the poverty rate is the highest in 20 years.

He said Democrats ran up federal budget deficits of $260 billion in five years but did not mention that the present annual deficit of the Reagan administration is $170 billion. Carter's last annual deficit was $58 billion.

Reagan said 6.5 million new jobs had been created in the last 19 months but did not mention that unemployment rose to a post-World War II high during the 1981-82 recession.

The president also attacked Democrats for the 1977 Social Security payroll tax increase but did not mention his proposal to cut Social Security benefits in 1981. Reagan later agreed to a bipartisan Social Security rescue package that accelerated tax increases.

Repeating a theme that has become his answer to Mondale's charge that Reagan would raise taxes in a second term, he promised that it is "time for tax increases to be an act of last resort, not of first resort."

Many of the charges and metaphors used by Reagan tonight have been sprinkled through speeches as far back as his first campaign for governor of California in 1966.

"If our opponents were as vigorous in supporting our voluntary-prayer amendment as they are in raising taxes, maybe we could get the Lord back in our schoolrooms and get the drugs and violence out," he said.

Reagan used a new line as he derided Mondale's "new realism," which the president said is indistinguishable from "old liberalism."

"We could say they spend money like drunken sailors, but that would be unfair to drunken sailors," Reagan said. "The sailors are spending their own money."

Addressing the tax issue that has dominated the early rhetoric of the presidential campaign, Reagan said: "Our tax policies are and will remain pro-work, pro-growth and pro-family. We intend to simplify the entire tax system, to make taxes more fair, easier to understand and, most important, to bring the tax rates of every American further down."

Vice President Bush, speaking before Reagan appeared, emphasized the tax issue even more bluntly, saying Mondale's declaration that he would raise taxes if elected "wasn't courage, just habit."

When Reagan referred to Bush, praising him for chairing a task force on reducing regulatory controls, the president called him "the finest vice president this country has ever had."

Reagan said reducing the risk of nuclear war was "the greatest challenge of all" facing the United States and the world, and he repeated declarations he made in the parliaments of Europe and Asia that "a nuclear war cannot be won and must never be fought."

Reagan appealed to the Soviet Union to join the United States in reducing nuclear arsenals but made no new proposals to accomplish this and warned that the Democrats would make "unilateral and unwise concessions to the Soviet Union" if they return to the White House.

The president devoted a longer passage in his speech to what he described as dangers posed to the world by the Soviets and potential communist takeovers in Central America "fueled massively by the Soviet Union and Cuba."

"Our policy is simple: we are not going to betray our friends, reward the enemies of freedom or permit fear and retreat to become American policies, especially in this hemisphere," Reagan said.

"None of the four wars in my lifetime came about because we were too strong. It is weakness that invites adventurous adversaries to make mistaken judgments," he said.

"America is the most peaceful, least warlike nation in modern history," Reagan continued. "We are not the cause of all the ills of this world. We are a patient and generous people. But for the sake of our freedom and that of others, we cannot permit our reserve to be confused with a lack of resolve."

Addressing the larger purposes of his presidency, Reagan said, "We are here to see that government continues to serve the people and not the other way around." That was a principal line of his earlier campaigns.

"We don't lump people by groups or special interests," Reagan said. "And let me add, in the party of Lincoln, there is no room for intolerance, and not even a small corner for anti-Semitism or bigotry of any kind. Many people are welcome in our house but not the bigots."

Reagan, 73, barred by the Constitution from seeking a third term if reelected, observed that tonight marked "the last time, of course, that I address you under these circumstances."

Then he said, referring to the First Lady, "Nancy and I will be forever grateful for the honor you have done us, for the opportunity to serve and for your friendship and trust."

Reagan's acceptance speech, which his advisers said he revised heavily, was the fourth he gave today in Dallas. The first was at a prayer breakfast.

Later, he spoke to the Republican National Hispanic Assembly luncheon, emphasizing the importance that the Reagan campaign committee places on this growing constituency.

Reagan, who usually has run more strongly in Hispanic communities than other Republican candidates, predicted that "Americans of Hispanic descent will flock to us in ever-increasing numbers."

The president went from the lunch to a meeting of the Republican National Committee where he gave a more partisan address and described Democrats as "the other party with its worn-out, discredited far-left ideology that caters to special interests."

Reagan is scheduled to fly to Chicago Friday to address the Veterans of Foreign Wars.