The essence of the peace-building efforts of the United Nations from the 1980s onwards included resolving underlying disputes between the belligerents, monitoring arms control agreements, and providing development assistance to maintain peace.

Option 1 states that the United Nations` peace-building efforts include resolving underlying disputes between the belligerents. This is correct as one of the main goals of the United Nations is to facilitate peaceful resolutions to conflicts.

Option 2 states that the United Nations` peace-building efforts include monitoring arms control agreements. This is also correct as the United Nations plays a crucial role in monitoring and enforcing arms control agreements to ensure weapons are not being used to escalate conflicts.

Option 3 states that the United Nations` peace-building efforts include providing development assistance to maintain peace. This is also correct as the United Nations often provides economic and development assistance to countries emerging from conflict in order to create stable conditions and prevent a return to violence.

Therefore, the correct answer is option 4, which states that the essence of the United Nations` peace-building efforts includes both monitoring arms control agreements and providing development assistance to maintain peace.