Short answers, pulled from the story.
Alexios I Komnenos was a Byzantine emperor who ruled from 1081 to 1118. Born around 1057, he seized the throne by leading a rebellion against Emperor Nikephoros III Botaneiates and died on the 15th of August 1118, succeeded by his son John II Komnenos.
In 1095, Alexios sent ambassadors to Pope Urban II at the Council of Piacenza requesting mercenary forces against the Seljuk Turks. Urban responded by preaching the First Crusade at the Council of Clermont later that year, producing far larger armies than Alexios had sought.
The Alexiad was a political and military history written by Anna Komnene, the daughter of Alexios I. She named it after her father. It is the primary historical account of his reign and campaigns.
Alexios defeated the Pechenegs on the 29th of April 1091 at the Battle of Levounion in Thrace by allying with a horde of 40,000 Cumans. This victory ended the Pecheneg threat to the Byzantine Empire.
In 1092, Alexios replaced the debased solidus with the hyperpyron, a gold coin of generally .900 to .950 fineness weighing 4.45 grams. He introduced it alongside the electrum aspron trachy, the billon aspron trachy, and copper coins to create a tiered currency system.
Anna Dalassene, the mother of Alexios I, was the effective administrator of the Byzantine Empire during his long military absences. Alexios had her crowned Augusta in an irregular move that bypassed his wife Irene Doukaina, and she was central to orchestrating the 1081 coup that brought him to power.