For the earlier period, I think it is worth reading Fred Donner's Muhammad and the Believers: At the Origins of Islam (2010) for an understanding of the confused world Islam was born in, followed by Patricia Crone's critical review of Donner's book - his book is a fantastic and easy read, but some of his suggestions are a bit out there. Why? Well, there are very few certainties about early Islam due to a lack of sources. Grand histories have been written before, but now historians are aware of how cautious we have to be when writing about such an enigmatic period of history. After Donner, Robert Hoyland's In God's Path: The Arab Conquests and the Creation of an Islamic Empire (2014) is the book to read on how the earliest caliphs built a very impressive empire in the seventh and eighth centuries. Again, this book is very readable, but Hoyland is also a historian working on the cutting edge of his field and included a lot of things that you will not be able to find in older books/on Wikipedia (and indeed often contradicts them!), so this is I think an essential read. Finally, Hugh Kennedy's The Prophet and the Age of the Caliphates: The Islamic Near East from the 6th to the 11th Century (2004) will give you a sense of the basic political narrative up to the eleventh century - it's basically the standard book given to undergrads studying this period, so like the other two books it should be a relatively easy read. Hopefully others will pop by and provide some suggested readings for books covering events after the eleventh century :)

There are tons of books on islamic history. What would you want to read, books by muslims or by non muslims, and which particular period of islamic history? I'll recommend some