These are broad time periods, not exact 100-year periods, and the names are frequently misleading. The Century of Strife, for example, lasted for 122 years (depending who you ask), and the Century of Peace saw many small-scale conflicts, usually internal.
Century of Arrival - colonists arrive, are scattered, attempt to regroup
Century of Struggle - colonists group up and struggle to survive on planet
Century of Cities - established settlements begin to reconnect and trade
Century of Leagues - settlements form into cohesive political groupings
Century of Strife - political groups fight over resources and ideology (Note: ends with defeat of Kodan by multi-league alliance)
Century of Peace - leagues reform and rebuild after war with the Kodan
Century of Ascent - largest leagues begin space race, colonize the moon
Century of Tumult - new and aggressive ideologies lead to lunar independence
Modern Day - Rylan Year 768, nearly 800 years since arrival in the star system
After arriving on the planet, the colonists clung to the resources and equipment they had managed to salvage from the ship. One settlement was uniquely blessed, having managed to preserve more than any others. This city-state, Rylos, made every effort to share this bounty with its neighbors, and proposed unification. They formed the Five-Star League, the first confederation on the planet, for which all modern nations are termed "leagues". The founding members were:
Rylos - built into some mesas, lots of tech; sacked and abandoned after war
Centauri City - league trade hub; destroyed by Kodan; resettled as Harlech
Schrade - left league to form Kingdom of Minegarde
Dundorma - left league to form Kingdom of Minegarde
Fellara - left league to form Fellaran Duumvirate with Harlech