More refs of interest on situations where the state doesn't have a monopoly on violence: 
 USMC Small Wars Manual, 1940ed.  A classic how-to manual for those little problems that requre sending in the Marines. Still widely read; on the mandatory reading list for USMC officers. Much of the book is about re-establishing a state monopoly on violence. There are sections on "disarmament of populations", and setting up a constabulary and a military government. 
 USMC Small Wars Manual, new rev. (to appear)  With all the small wars lately, the Marines are updating their manual. It's not out yet.
 "The Modern Nation State and Regimes of Violence: Reflections on the Current Situation" . A recent paper on the subject by Kossler, a German academic writing for a Japanese audience. Pages 15-18 have a good summary of the history of the concept - Hobbs, Weber, Marx, etc. He views the "monopoly on violence" as the result of the consolidation process which turned Europe from a collection of feudal regions into nation-states. Rather than trying to define "legitimate" violence, Kossler speaks of the "public dimension of violence".  Kossler also sees an economic dimension: "The guarantee of sound market conditions therefore is also dependent on the  effective exercise of sovereignty by the state.".  After covering the classic position, Kossler points out that non-state actors mess it up: "The post-9/11 situation forces important and disconcerting qualifications on this rather conventional picture. This goes back to the fact that an act of outrageous violence emanating from a non-state source which cannot be defined in territorial terms has been interpreted as an act of war, to be countered by military means, including the targeting of certain state-bounded territories, such as Afghanistan and later Iraq." He also mentions the rise of "networked organizations", including crime cartels that operate across borders, as challenging state monopolies on violence.
 In 2004, George Will wrote, about the US-Iraq war, "The first task of the occupation remains the first task of government: to establish a monopoly on violence."  Because that effort wasn't successful, there's a lot of later material on what happens when the state can't establish a monopoly on violence. See also Arab Spring. 
 Please read some of these and contribute to the article. Thanks.