A Muv-Luv Extra anthology by DNA Media Comics. 

Takeru and Sumika have been neighbors and friends since they were little, but when a mysterious girl arrives, and is found in bed with Takeru, their daily lives will be thrown into chaos.

In Muv-Luv Alternative, Takeru wakes up three years after the end of Muv-Luv Unlimited to find himself back in his room. Although he first thinks that everything that had happened to him was a dream, he soon feels that something is wrong, and leaves the house to find that he has been sent back in time to the beginning of the events in Unlimited. Unwilling to accept something like Alternative V, he decides to help professor Kouzuki to complete Alternative IV and save mankind. 
(Source: Wikipedia)

Light novel adaptation of the visual novel trilogy, covering Muv-Luv Extra, Unlimited and Alternative.
 
Shirogane Takeru is a typical high school student with a lazy attitude and a love for the virtual reality mecha battle game Valgern-on. Even though he didn't really want it, he's popular in school mainly due to his daily fights with his childhood friend (Sumika) attracting too much attention. His life takes an unexpected turn when he finds a girl named Meiya he doesn't remember ever meeting in his bed one morning. She's later revealed to be the heiress of one of the biggest corporations in Japan. She immediately moves to his house and starts changing his life for the good with her one-track-mind and unlimited resources... 
 
(Source: VNDB)

Focuses mostly on the past and upbringing of Tsukuyomi Mana, and to a lesser extent, Maya. Showcases their meetings and relationship with Meiya and Yuuhi, and shows their perspective throughout some of the events from Alternative as well. 

A short after story to Meiya's route in Extra. Focuses on overburdened Takeru (and Tsukuyomi) trying to spend some time alone with Meiya.
 
Note: Originally published in Dengeki Muv-Luv, finished in the second issue.

Comic Anthology by 10 Muv-Luv writers and artists, made up from the various Muv-Luv and âge entries that were available at the time of release.

A story of the bonds between those who fight, in a world pushed to its limits. On one of the countless parallel worlds that exist throughout spacetime, humanity has fought a decades long war against the BETA, hostile extraterrestrial invaders, using humanoid fighting machines called Tactical Surface Fighters. This is a story of how humanity lives and dies while on the brink of extinction… 
 
(Source: Crunchyroll)

One day Shirogane Takeru wakes up late, wondering why Sumika or Meiya didn't wake him up that morning. Not seeing any signs of them he gets a bit worried, and goes out of his house only to see the town he lived all his life in ruins, and finds a giant robot destroyed outside of his house. After getting past the initial shock he convinces himself that it must be a dream and decides to enjoy it as much as he can. Soon he finds out the terrible truth behind the reason the world is in ruins, and meets people that look exactly like his friends from his original world. 

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