I can certainly recommend 'The Early Abbasid Caliphate: A Political History' as an excellent resource, suitable as both an introduction and a more in-depth study for anyone wanting to understand Abbasid history. However, I found the approach taken in the last two chapters somewhat confusing, and it's rather disappointing that the detailed coverage of the Caliphs effectively concludes with al-Ma'mun, leaving one wishing the narrative had extended further into the period.