What were Muawiyah's aim and achivements?
Muawiyah, who lived from 602-680, was a Muslim, the fifth Sunni Caliph, and as Caliph founded the Umayyad Dynasty and established its capitol not in Mecca nor in Medina, but in Damascus.
He was from a prominent Meccan family ut converted to Islam after the Battle of Badr when it seemed certain Muhammad would gain control of Mecca. Later he was made governor of Syria and fought against the fourth Caliph, Ali. After Ali's assassination, Muawiyah was recognized as the next Caliph. And he set his son Yazid as his successor as the next Caliph, breaking the tradition of selecting Caliphs by consensus and for their religious (not merely political) leadership.
Sunni and Shia Muslims differ sharply in their views of Muawiyah. For Shia Muslims, Muawiyah represents tyranny. He is viewed as a usurper who sent his son Yazid to massacre Hussayn and his followers at the Battle of Karbala in 680.
So views on him differ and there are a number of questions about his aims. We can point to his establishment of the Umayyad Dynasty in Damascus as his single biggest accomplishment, but one should also note his role in the death of Ali and the conflict with the early Shia community.