To build the bes hamidash and establish malchus bes David melech yisrael and the Torah in Yerushalayim, yehuda and possibly all of eretz Yisrael.
Hadrian (starting 58 years after churban) originally supported this idea, as it would get the annoying rebellious jews out of the diaspora, where they were causing major trouble. Just 20 years earlier, in the Kitos war (Andreas Lukas was Moshiach then for Egyptian jews), the jews killed most of the gentiles in Egypt, Libya – called Cyrene – and Cyprus, in response to anti Jewish actions etc… They failed dismally (like most Messianic jewish rebellions – except the Macabees and the modern zionists), and were almost entirely annihilated (the rest sold as slaves).
Hadrian sent his relative, Aquilas, to help the jews come back and rebuild. Long story short, he became a Ger and explained the Torah in Greek.
Bar Kochba was Moshiach and rebuilt the third bes hamikdash in Yerushalayim. It stood for 2.5 years, after which Hadrian destroyed it (65 after churban), causing Him to flee to Betar, where they were eventually mostly annihilated (the rest sold as slaves – mainly to Europe)
What caused Hadrian to change his mind? Good question!