Eureka Seven vol. 1: The New Wave is the first in a trio of games set in the Eureka Seven anime world. A direct sequel, Eureka Seven vol. 2: The New Vision, was released in 2006. It is a prequel; the storyline takes place before the events of the anime series.
The main player character throughout the game is Sumner Sturgeon, a young man newly transferred to a new military academy which specializes in LFO pilot training. LFOs, giant mechanical humanoid weapons, fly using the same mechanism as the human 'Lifters' in the game: jet-propelled flying surfboard-like devices.
The main character is Sumner Sturgeon, the son of the renowned Bernard Sturgeon. Sumner starts out at a military training academy, dubbed New Wave (or NW). That is where he meets his love interest, a girl by the name of Ruri. Sumner’s teammate, Hooky, immediately gets jealous and challenges him for Ruri's heart in the championships of New Wave academy. At the championships, Sumner finds out that Ruri is leaving New Wave. She says that he wouldn't understand it until he owned his own LFO and leaves him with a kiss and a picture. Sumner wins the championships regardless, only to be recruited by the illustrious Sawyer Team, the military branch that New Wave has been training him for. From there on out he pilots his KLF on various missions that test how well he knows his LFO, such as taking out a bandit group situated in mines, getting hard evidence against a black market trade, and protecting his city from various disruptions. Later on, Sumner’s old teammates join Sawyer Team. There are then six people on Sawyer Team, and Hooky still dislikes Sumner.
After a series of missions, Sumner eventually meet up with characters from the anime, including Holland, to whom he bequeaths the advanced Nirvash LFO he stole from the military, Moondoggie, who like Sumner appears in the sequel, and Eureka. The game's final missions find him piloting the Nirvash.
Source: Wikipedia, "Eureka Seven vol.1: New Wave", available under the CC-BY-SA License.