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 its former glory, unfortunately the Jedi Temple was mostly destroyed by Kylo Ren and the Knights of Ren.
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, realising 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 due to the manipulations of the mysterious Supreme Leader Snoke. As Snoke preyed on Ben's internal conflict, Ben then became known as Kylo Ren. Kylo, aided by the Knights of Ren, killed most of Luke's apprentices.
Luke watched in horror as he was unable to stop the Jedi massacre, Luke and his astromech droid R2-D2 watch as most of the Jedi Temple was burning, Luke's apprentices, the ones who survived the Jedi massacre went into hiding until the time was right for them to come out of of exile, Luke on the other hand, when in search of Ahch-To Jedi Temple possibly seeking guidance from the spirits of the ancient Jedi on how to rebuild the Jedi Order. Luke would remain in hiding on Ahch-To, until the time was right for him to come out of self-exile.