Core Legal Answer & Context: The United Nations General Assembly (UNGA) is the main deliberative, policymaking, and representative organ of the UN. Comprising all 193 member states, each with one vote, it serves as a forum for multilateral discussion on international issues covered by the UN Charter.

Powers and Functions:

1. Deliberative and Recommendatory: Discusses any questions or matters within the scope of the UN Charter and makes recommendations to member states or the Security Council (Article 10).
2. Peace and Security: Considers principles of cooperation in the maintenance of international peace and security, including disarmament, and can make recommendations (Article 11). It can also take action if the Security Council is deadlocked (Uniting for Peace Resolution).
3. International Cooperation: Initiates studies and makes recommendations for promoting international cooperation in political, economic, social, cultural, educational, and health fields, and assisting in the realization of human rights (Article 13).
4. Budgetary: Considers and approves the budget of the Organization and apportions expenses among members (Article 17).
5. Supervisory: Receives and considers reports from the Security Council and other UN organs.
6. Elective: Elects non-permanent members of the Security Council, members of ECOSOC, and, concurrently with the Security Council, judges of the ICJ. It also appoints the Secretary-General upon the recommendation of the Security Council.
7. Charter Amendment: Can recommend amendments to the UN Charter.

Relevant Statutes and Sections:

1. UN Charter, Chapter IV (Articles 9-22): Specifically outlines the functions and powers of the General Assembly.

Important Landmark Cases:

1. Certain Expenses of the United Nations (ICJ Advisory Opinion, 1962): The ICJ affirmed the UNGA's power to authorize expenditures for peacekeeping operations, even if the Security Council had primary responsibility for peace and security, clarifying the UNGA's financial and operational role.
2. Uniting for Peace Resolution (1950): Expanded the UNGA's role in peace and security, allowing it to recommend collective measures, including the use of armed force, if the Security Council fails to act due to a veto.

Clear Conclusion: The UN General Assembly possesses broad deliberative, supervisory, financial, and recommendatory powers. While its resolutions are generally non-binding (except for internal UN matters), its universal membership and extensive mandate make it a crucial forum for shaping international norms, promoting cooperation, and influencing global policy across a wide range of issues.