Luke Skywalker's Jedi Temple, is an unnamed Jedi Temple located on an unknown planet, sometime after the end of the Galactic Civil War, Luke used this Jedi Temple to train a new generation of Jedi Knights, in order to restore the Jedi Order to it's former glory, unfortunately the Jedi Temple was destroyed by a lightning storm in the night Ben Solo fell to the dark side, and most of Luke's students were killed during this event.
Sometime after the Battle of Jakku, Jedi Master Luke Skywalker discovered or built this Jedi Temple on an unknown planet, to serve as a Jedi academy; in order to train a new generation of Jedi Knights and establish a New Jedi Order, realizing that the old Jedi teachings as well as the old code were flawed and to avoid the New Jedi Order from making the same mistakes as the Old Jedi Order - Luke altered some of the Jedi teachings and code.
The first of Luke's students was his nephew, Ben Solo and several other Force-users, unfortunately, his nephew fell to the Dark side when Ben when discovered that his uncle, Luke wanted to kill him, because he was afraid of how stronger connection to the Dark side of the Force was. Ben attacks Luke in self-defense, and collapses the hut they were in, he then (apparently) killed most of Luke's apprentices. Unbeknownst to everyone, Ben did not actually massacre all his fellow apprentices, as they were killed by a lightning storm (possibly made by Sheev Palpatine).
The three survivors that were not in the Temple when the storm happened pursued Ben Solo for attacking their master Luke. Two are later killed confronting him and one is murdered by Ren, the former leader of the Knights of Ren.
Luke was in horror as he was unable to stop the death of his apprentices, Luke and his astromech droid R2-D2 watch as most of the Jedi Temple was burning, Luke went in search of the Ahch-To Jedi Temple, as he was guilt ridden over his students' deaths, Ben's fall to the dark side, and his other students' disappearance. Luke would remain in hiding on Ahch-To, until the time would come when he dies; so that the Jedi Order would end with him.