From Halopedia, the Halo wiki
2552 was a year in the 2550s in the 26th century. It was the ultimate year of the Human-Covenant War, during which the humans of the United Nations Space Command nearly saw utter defeat and extinction, though the tide turned, and with significant help from the Sangheili, they managed to win the war. The Covenant were at the peak of their power and reach in 2552, with major assaults on the human Inner Colonies and an invasion followed by a prolonged engagement on their home planet, Earth. During the battle at Installation 04, the galaxy found its first large outbreak of the Flood threat in over a hundred thousand years. Over two months later, an even larger outbreak occurred at Installation 05.
The war finally drew to a close at Installation 00, known more commonly as the Ark, with the humans and Sangheili attempting to kill the Prophet of Truth, before he could activate the remaining Halo installations. The alliance was successful in their mission against the Covenant.
May 14 through May 19
After July 5
Early August (sometime from the 6th to the 12th)
After the recovery of a Forerunner device on Reach, the members of an organized resistance comprised of Spartans from Reach and survivors of the Battle of Installation 04 are in some sort of time anomaly, causing them not to be in the "correct timeline". What is known is that the events take place with the possession of the device after September 7.
October 21 through November 17
October 20 through November 2
The end of 2552 saw the bloodiest period of the Great War and the beginning of the end. The Prophet of Truth was killed in the later months along with a sizable Covenant armada, leaving the Covenant forces crippled and leaderless as well as the full destruction of the Gravemind and its Flood forces.
November 8 through November 15
November 8 through November 17
The Great Schism
Quarantine of the Flood