Kariya's older brother, the father of Shinji Matou. With Zoken, he oversees Sakura's magical training to become the family's heir.   

As the Fourth Holy Grail War rages on with no clear victor in sight, the remaining Servants and their Masters are called upon by Church supervisor Risei Kotomine, in order to band together and confront an impending threat that could unravel the Grail War and bring about the destruction of Fuyuki City. The uneasy truce soon collapses as Masters demonstrate that they will do anything in their power, no matter how despicable, to win.
 
Seeds of doubt are sown between Kiritsugu Emiya and Saber, his Servant, as their conflicting ideologies on heroism and chivalry clash. Meanwhile, an ominous bond forms between Kirei Kotomine, who still seeks to find his purpose in life, and one of the remaining Servants. As the countdown to the end of the war reaches zero, the cost of winning begins to blur the line between victory and defeat.
 
(Source: MAL Rewrite)

War of the Holy Grail - Pursuing the power of the "Holy Grail" which grants a miracle, this is a contest in which seven magi summon seven Heroic Spirits to compete for it. In that battle whose conclusion was postponed three times, now, the fourth war commenced again. Entrusting their dearest wish of victory, the magi joined the battleground called "Fuyuki", but amongst them, there was a man who was always alone, and could not find out the meaning behind his fights. His name was Kotomine Kirei. Not comprehending the guidance of fate, Kirei was lost, and had kept questioning. Why someone like his was given the Command Seals. However, the fate of his fights crossed Kirei's path with a nemesis by chance. That person is - Emiya Kiritsugu. A man who was sterner than anyone else, more merciless than anyone else, and who sought the miracle of the Holy Grail. 

Merely recited in fragments in Fate/Stay Night, this is the Fourth War of the Holy Grail 10 years ago. The truth which unfolded behind the battle between Shir&#333;'s foster father, Rin's father, and the younger Kotomine Kirei, is finally revealed...

Based on the third route of Fate/stay night.

The Fourth Holy Grail War has begun, and seven mages must summon heroes from history to battle each other to the death. Only one mage-and-hero pair will remain to claim the Grail and have their wishes granted! Kiritsugu Emiya was once an assassin but now fights in this war to save the world from those who would destroy it with the Grail’s power. 
(Source: Dark Horse)

Byakuya Matou