1. Chadwick, J. (1976). The Mycenaean world. Cambridge: Cambridge University Press.
Chadwick is one of the greats of Mycenaean archaeology, with dozens of books and journals dedicated to the period. This work provides good indtroduction to the political and social organization of the Mycenaean world, while also going more indepth on the subject.
2. Rutter, J. B., & Demakopoulou, K. (1990). The Mycenaean World: Five Centuries of Early Greek Culture, 1600-1100 B. C. American Journal of Archaeology, 94(3), 499. doi:10.2307/505813
Like Chawick's work, this is a more general text on the Mycenaean period. In the article, Demakopoulo and Rutter also provide introduction level material on Mycenaean political and social organization mixed with more indepth info.
3. Hooker, J. (2014). Mycenaean Greece (Routledge Revivals). doi:10.4324/9781315796666
Another excellent work on Mycenaean Greece. This journal article has more indepth information and less introdutionary material.
During the Late Helladic period, Mycenaean civilization developed into a proto-state model. Characteristics of this development include: centralized social and political organization, rulers dominating elites, the ruled fulfilling obligations to the rulers, and a society sustained by a common ideology. Politically, territories were controlled by palaces which acted as administrative centers that maintained a network of settlements of lessening hierarchical status. The Mycenaean society was stratified, the top being a king, down through the religious, political, and military elite to the lowest subjects and slaves.