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  ====Season 1====
  After Tyrion Lannister's arrest by Catelyn Stark, Tywin sends Gregor Clegane to raid Catelyn's homeland, the Riverlands.
  Later on, Jaime is seen in Tywin's camp reading a royal command issued by Eddard Stark on behalf of the crown summoning Tywin to appear before the court to answer for an attack on the Riverlands by his bannerman Gregor Clegane.
  Tywin chastises Jaime for openly attacking Eddard Stark, when Jaime states he did so on hearing of Tyrion's arrest.
  He gives half of his men (30,000) to Jaime Lannister to besiege House Tully's ancestral home of Riverrun. 
  Jaime is surprised that Tywin places such a high value on Tyrions life, but Tywin states that he is merely doing this to protect his family's honor, as allowing an other house to keep a member of Lannister family prisoner would weaken their family's position.
  Tywin is tricked by Robb Stark into taking his men to the Trident where he believes Robb Stark intends to fight his army. Instead, Robb Stark leads his forces to Riverrun, where he defeats and captures Jaime Lannister.
  When Joffrey Baratheon ascends as king, he executes the former Hand, Eddard Stark and names Tywin as his Hand. 
  Tywin who currently has only half of his army is now engaged in multiple conflicts, with Robb Stark in the North and Stannis & Renly Baratheon in the South.
  Tywin cannot make peace with the Baratheon brothers as they are staking for the claim of Kingship of the Seven Kingdoms.
  Eddard's  execution by Joffery on the other hand has prevented Tywin from what would have been the best option of suing for peace with Northern Lord and Riverrun. Realizing this Tywin sends Tyrion to King's Landing as acting Hand, while he decides to regroup at Harrenhal with all his forces and continue the campaign in the Riverlands against Robb Stark who now hold his son captive.