The Second Battle of Harvest, also known as just simply the Battle of Harvest, was humanities first attempt to recover the planet Harvest from the Covenant, who wiped out the existing colony and killed tens of thousands of civilians a year earlier.
In an effort to limit the ability for the Covenant to discover human colonies, including the inner colonies and Earth, the Cole Protocol was established to wipe all ship navigation data when the UNSC came into contact with any Covenant forces.
Operation: RED FLAG was a planned operation by both the Office of Naval Intelligence and the UNSC to use Spartans to capture a Covenant ship, use it to penetrate into Covenant space, and capture a Hierarch, with the intent of using the Prophet to broker a cease-fire.
Operation: FIRST STRIKE was a mission undertaken by John-117 and several other Spartan-IIs to infiltrate and destroy the Covenant space station Unyielding Hierophant and associated armada of over 500 warships in the Tau Ceti system prior to the Covenant's invasion of Earth.
The Battle of Installation 05 was an engagement between the Covenant forces, including those that fled the Battle for Earth, High Charity, and the Second Fleet of Homogeneous Clarity, and the UNSC-allied forces, including the UNSC In Amber Clad led by Miranda Keyes, and the Fleet of Retribution led by the Arbiter Thel 'Vadam.