The annual meeting of the U.N. General Assembly opens Tuesday, with more than 100 world leaders gathered to discuss a wide range of issues including post-Gadhafi Libya, the Palestinian statehood application and non-communicable diseases.

Topping the agenda Tuesday will be a summit on Libya's political transition. U.S. President Barack Obama and other leaders will gather to discuss how the global community can best help Libya rebuild following the overthrow of longtime leader Moammar Gadhafi and months of unrest across the country.

Libya will be represented by National Transitional Council chairman, Mustafa Abdel Jalil. The U.N. Security Council voted overwhelmingly last week to turn over Libya's General Assembly seat to the country's new government, effectively recognizing the end of the Gadhafi regime.

The question of U.N. membership for a Palestinian state will dominant the conversation during the 66th annual session of the General Assembly. Palestinian President Mahmoud Abbas will deliver his application on Friday, when he is also expected to address the assembly.

Israeli Prime Minister Benjamin Netanyahu is leading the way, along with the U.S., to block Palestinian efforts for membership. He will take the podium Friday following Mr. Abbas.

U.S. President Barack Obama arrived in New York Monday afternoon with a full schedule of meetings. Mr. Obama plans to meet with NTC leader Jalil. Mr. Obama also will meet Salva Kiir, president of the world's newest country, South Sudan. Later in the week President Obama is to meet with Israeli Prime Minister Benjamin Netanyahu. Mr. Obama is to address the U.N. General Assembly Wednesday.

Events focusing on global health and women's issues kicked off Monday. Leaders gathered for a two-day meeting to discuss the world's biggest killer, non-communicable diseases. This is only the second time the General Assembly has focused on a health issue. U.N. Secretary-General Ban Ki-moon called the increasing number of deaths from these preventable and treatable diseases “alarming.”

Prominent female politicians led by Secretary of State Clinton and Brazil's President Dilma Rousseff also met and urged a greater political role for women across the world. According to the U.N., women count for less than 10 percent of world leaders.