Short answers, pulled from the story.
Alexios I Komnenos seized the throne on the 1st of April 1081 after marching into Constantinople with a small army. His mother Anna Dalassene orchestrated a deception involving pilgrims and stolen imperial horses to buy time for gathering troops.
Alexios I Komnenos secured an alliance with Holy Roman Emperor Henry IV who paid 360,000 gold pieces to attack the Normans from Italy. This German intervention forced Robert Guiscard to return home allowing the Byzantines to recover most lost territories by 1085.
Alexios I Komnenos achieved a decisive victory at the Battle of Levounion with help from 40,000 Cuman allies in April 1091. The battle ended the Pecheneg threat permanently after they had previously forced the emperor to sign a truce and pay protection money.
Alexios I Komnenos introduced the hyperpyron gold coin in 1092 to replace the debased solidus that had circulated throughout the empire for decades. This new currency maintained a fineness level between .900 and .950 while weighing approximately 4.45 grams per piece.
Anna Komnene recorded her father's reign in the Alexiad which remains the primary historical source for this period. Her account documents the restoration efforts and numerous conspiracies faced during his thirty-seven year reign.
Alexios I Komnenos died on the 15th of August 1118 after managing to preserve the state despite facing numerous pretenders and conspiracies. His death marked the end of his long reign which stabilized the empire and inaugurated over a century of imperial prosperity.