From the Wiki:
Fire Emblem: Three Houses is a tactical role-playing game, developed by Intelligent Systems with support from Koei Tecmo Games. The game was published worldwide for the Nintendo Switch by Nintendo on July 26, 2019. The game is the fifteenth game in the Fire Emblem series, and the first for home consoles since Fire Emblem: Radiant Dawn in 2007.
The game takes place on the continent of Fódlan. The landmass is divided into three rival nations who are now at peace: the Adrestian Empire to the south and west, the Holy Kingdom of Faerghus to the north, and the Leicester Alliance to the east. At the center of the continent is the Garegg Mach monastery, home of the Church of Seiros and its Officer's Academy. The academy comprises three houses, each populated with students from their respective nations: The Black Eagles, Blue Lions or Golden Deer. The player character's name and gender may be chosen by the player, but is named "Byleth" by default. Once part of a mercenary group led by their father Jeralt, Byleth is offered a position to teach at the academy after an unexpected incident. As they start to teach their students, including Edelgard, Dimitri, and Claude, the heirs of their respective home countries, Byleth begins to see Sothis, a mysterious girl only they can see. [Source: Wikipedia]
The Verge: Fire Emblem: Three Houses is secretly the best Harry Potter game
IGN: Fire Emblem: Three Houses offers an incredible amount of choice both on and off the battlefield alongside a thrilling story. [9.5/10]
GameSpot: Fire Emblem: Three Houses is a game that is mechanically complex, consistently rewarding, and very hard to put down. [9/10]
Kotaku: Fire Emblem: Three Houses is a game for interesting times.
Update: Replaced pictures with animated GIFs of Gameplay footage.
Update 2: Replaced banners, etc.