There are a lot of controversies in Islam about this great man. But this is separate from the extraordinary achievements he made in his lifetime. Mu'awiya is a powerful figure in the history of Islam. Mu'awiya ibn Abi Sufyan is undoubtedly the most elusive and ambiguous of the early caliphs.
Furthermore, he was a political genius at a time when nothing else could have saved the Islamic Empire from dissolution, regardless of what we think of him as a ruler and a man (a matter on which opinions disagree sharply, to put it gently). He goes through numerous stages in his life and work.
There is a wealth of information on Mu' awiya ibn Abi Sufyan in this book, from his life and times in the Islamic Empire through his character, controversies, and reign.