Tengen Toppa Gurren Lagann (abreviated to TTGL) is the story of Simon and the Gurren Brigade. Living underground for reasons they cant comprehend Kamina dreams of going to the world above. One day a giant mechanical beast falls into their cavern along with a busty teenager called Yoko. With the help of Yoko, Kamina and a small machine which Simon finds and is baptized as "Lagann" they manage to defeat this threat. Following these events, Simon, Kamina and Yoko end up in the surface, where Simon and Kamina learn that it is controlled by beastmen and that Yoko is part of the resistance against them.
After the above events comes the final part of the story, where the Gurren Brigade must now face threats from space to protect their world.
TTGL has 3 arcs, the first 2 arcs being on a level comparable to most shonen verses. At this point the verse is only in hypersonic territories and has mountain to country level power more or less. However in the 3rd part after the timeskip massive power boosts are introduced, eventually reaching universal threat levels. (Possibly even higher in the movie version retelling)