Core Legal Answer & Context: International Humanitarian Law (IHL), also known as the law of armed conflict or the law of war, is a body of international law that seeks to limit the effects of armed conflict for humanitarian reasons. It protects persons who are not or are no longer participating in hostilities and restricts the means and methods of warfare.

Core Principles of IHL:

1. Distinction: Parties to a conflict must at all times distinguish between combatants and civilians, and between military objectives and civilian objects. Attacks must only be directed against combatants and military objectives. Civilians and civilian objects must not be attacked.
2. Proportionality: Even legitimate military targets cannot be attacked if the expected civilian casualties or damage to civilian objects would be excessive in relation to the concrete and direct military advantage anticipated. The harm to civilians must not be disproportionate to the military gain.
3. Necessity (Military Necessity): Military operations must be necessary to achieve a legitimate military objective. Force used must be the minimum necessary to achieve that objective, and actions not required for military purposes are prohibited.
4. Humanity (or Unnecessary Suffering): Prohibits the use of weapons, means, and methods of warfare that are of a nature to cause superfluous injury or unnecessary suffering. This principle underpins the prohibition of certain inhumane weapons.
5. Precaution: Parties to a conflict must take all feasible precautions in attack and defense to avoid, or at least minimize, incidental loss of civilian life, injury to civilians, and damage to civilian objects.

Relevant Statutes and Sections:

1. Geneva Conventions of 1949 and their Additional Protocols of 1977: The cornerstone of IHL, protecting wounded and sick in armed forces, prisoners of war, and civilians.
2. Hague Conventions of 1899 and 1907: Primarily concern the means and methods of warfare.
3. Rome Statute of the International Criminal Court (1998): Defines war crimes, crimes against humanity, and genocide, enforcing IHL.

Important Landmark Cases:

1. Legality of the Threat or Use of Nuclear Weapons (ICJ Advisory Opinion, 1996): The ICJ affirmed the fundamental principles of IHL, particularly distinction and proportionality, as applicable to all weapons, including nuclear weapons, emphasizing their enduring relevance.
2. Tadić Case (ICTY Appeals Chamber, 1999): The International Criminal Tribunal for the former Yugoslavia extensively discussed the application of IHL in both international and non-international armed conflicts, clarifying the principles of distinction and proportionality.

Clear Conclusion: The core principles of IHL—distinction, proportionality, necessity, humanity, and precaution—are designed to strike a balance between military necessity and humanitarian considerations during armed conflict. They aim to protect non-combatants and limit suffering, ensuring that even in the brutality of war, there are fundamental rules to uphold human dignity.