Raraiya Monday is a girl who suddenly appears on Earth piloting the G-Self. An amnesiac, she is given the name "Monday" when Captain Dellensen takes her under his protection on a Monday. She is one of three people who can pilot the G-Self.

(Source: Gundam.info)

Some time has passed since the end of the Universal Century, a history marked by space colonization and space warfare. 
Humanity's prosperity, which ushered in a new era known as Regild Century (R.C.), was believed to endure alongside the global peace. 
 
It is the year R.C.1014. 
 
The Capital Tower is an orbital elevator that rose above the Earth's surface and linked Earth and space. As the conduit of the Photon Battery energy source to the surface, it is regarded as sacred. 
 
Bellri Zenam is in the middle of training for the Capital Guard (established to protect the Capital Tower), when the tower is attacked by the G-Self — a highly maneuverable mobile suit with technology that is not from any known country. 
 
Bellri, who joins the battle in the maintenance mobile suit Recten, successfully captures the G-Self. However, Bellri feels something for the space pirate girl named Aida Surugan who piloted the G-Self. It is the same feeling he has for the G-Self, even though he supposedly never seen it before. The G-Self, which should only be operable under specific conditions, is somehow started up by Bellri. 
The objective of Aida and the space pirates who attacked the Capital Tower, and the fate followed by Bellri who was chosen by the G-Self, will lead to truths that will shake the entire Regild Century era.
 
(Source: Anime News Network)
 
 
The first 3 episodes premiered theatrically from August 23, 2014 to September 5, 2014 with the regular TV broadcast starting on October 3, 2014.

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The first film compiling the Gundam: G no Reconguista TV series.

The second film compiling the Gundam: G no Reconguista TV series.

The third film compiling the Gundam: G no Reconguista TV series.

The Universal Century, with its history of colonization and wars, passes into posterity, and time flows on.
 
Mankind enters a new age of seemingly endless peace and prosperity called the "Regild Century."
 
The year is R.C. 1014. The Capital Tower, an orbital elevator, connects earth and space. Due to its role in supplying Earth's power by transferring Photon Batteries from space, it is worshiped with a religious fervor. Bellri Zenam, a cadet in the Capital Guard formed to protect Capital Tower, is participating in his first non-simulated exercise when he is attacked by the powerful but unaffiliated "G-Self" mobile suit. He manages to capture the G-Self while piloting a "Recten" maintenance mobile suit. However, seeing the G-Self's pilot, a young space pirate named Aida Rayhunton, stirs something within him, as does the G-Self which he was sure he'd never seen before. Why does the G-Self accept Bellri as a pilot?
 
Aida's mission to attack Capital Tower. Bellri's destiny as a chosen pilot of the G-Self. The truth which will shake the Regild Century.
 
It was all the beginning of the Reconguista.
 
(Source: Gundam.info)