The annual gathering of world leaders at the U.N. General Assembly debate gets underway this week in New York, with dozens of meetings and events taking place on its sidelines. This will also be Barack Obama's first visit as U.S. president to the United Nations, where he will be playing a very high-profile role.

By all accounts, this week will be one of the busiest in U.N. history.

Events get underway Tuesday, when Secretary-General Ban Ki-moon hosts a summit on climate change that more than 90 presidents and prime ministers are expected to attend.

Negotiations are underway on a global climate treaty that seeks serious carbon-emission reductions. Governments hope to have it finalized by December when they meet in the Danish capital, Copenhagen. But the secretary-general says he is worried that the pace of negotiations is too slow, and he is convening the summit to give them a political boost.

"We want world leaders to show they understand the gravity of climate risks, as well as the benefits of acting now," he said. "We want them to publicly commit to sealing a deal in Copenhagen. And we want them to give their negotiating teams marching orders to accelerate progress toward a fair, effective, comprehensive and scientifically ambitious global climate agreement in Copenhagen."

On Wednesday, the full 192-members of the international community will begin the 64th annual debate in the General Assembly.

President Obama will make his highly anticipated address on that first morning. His administration has actively sought to embrace multi-lateralism and improve its relationship with the U.N. as an institution. U.S. Ambassador to the United Nations Susan Rice says the president's remarks will reflect this.

"He will then deliver his historic first speech to the United Nations General Assembly, and address his view of international cooperation in the 21st century and the need to move beyond old divisions to focus on the future," said Rice. "He will lay out a new direction that he has set for American foreign policy, and talk about our mutual responsibilities to make progress on several key priorities that will advance our common security and prosperity."

In addition to attending the opening of the climate change summit and addressing the General Assembly, President Obama will chair a meeting of the U.N. Security Council on the subject of nuclear non-proliferation and disarmament. The United States holds the rotating presidency of the council this month and this meeting will be the first time a U.S. president has chaired a council session.

On the margins of all the official events, President Obama will have bilateral meetings with several other world leaders, including Japan's new prime minister, and the presidents of China and Russia.

He will also host a trilateral meeting with Israeli Prime Minister Benjamin Netanyahu and Palestinian Authority President Mahmoud Abbas, in an effort to continue U.S. efforts to re-launch Israeli-Palestinian negotiations.

While President Obama's presence has generated a lot of excitement, some other world leaders are not receiving such a warm welcome.

Controversy has surrounded the visit of Libyan leader Moammar Gadhafi after he welcomed home Libyan national and convicted Lockerbie bomber Abdel Basset al-Megrahi, who was released early from a British prison because he is dying from cancer. 

Iranian President Mahmoud Ahmadinejad's presence at the General Assembly always prompts demonstrations against his regime's human-rights abuses. This year is not likely to be any different, after disputed election results returned him to office for a second term.

Security will be extremely tight in the city with more than 120 presidents and prime ministers expected to be passing through the United Nations this week.