Gate: Jieitai Kanochi nite Kaku Tatakaeri

A gate appears in Tokyo's Ginza district sometime in the 21st century. From the gate pours out monsters, knights from middle-age Europe, and other fantasy-like beings, and they kill many of the citizens of Tokyo. This event is known as the Ginza Incident.
The government sends a small group of soldiers from the Japanese Self-Defense Forces (a replacement for Japan's military) to the alternate world beyond the gate. Led by otaku soldier Youji, they find that the villages in the world are being attacked by a dragon. An elf girl who is a survivor from the dragon's rampage joins the group in their travels across the dangerous new world.
from Manga Updates
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Notes

Alternative Names: GATE, Gate: The Self-Defense Forces Fight Like This in That Place
Author: Takumi Yanai
Artist: Izuka Daisuke
Genre: Action, Adventure, Comedy, Drama, Fantasy, Mature, Romance
Demographic: Seinen
Adapted into the anime, Gate: Jieitai Kanochi nite Kaku Tatakaeri