This short pamphlet consists of a polemic against the New Left followed by a laying-out of Arendt's own views on the relationship between violence and power. The first part consists of an attack on student radicals with intermittent swipes at Fanon and Sartre. The latter draws distinctions between power, violence and authority, before presenting an argument that the state is based on power rather than violence and that it depends on consent. It also presents arguments for a civic "political" commitment against both bureaucracy and new social movements. The argument is dependent on Arendt's "The Human Condition" at several points, and reads as rather speculative and assertive rather than demonstrative.
There are several reasons I'm not particularly impressed with this pamphlet. The first is that the author basically makes a straw-man of her opponents. The views attributed to the amorphously defined "New Left" - such as that violence founds society, that it is a means to achieve immortality, that violence is natural, that a primordial will to dominate is fundamental - are not properly sourced and basically do not occur in the literature Arendt is implicitly referring to (Marcuse, Sartre, Fanon, Negri, Situationism, etc). She rarely references her opponents at all, ignoring their theories - the only exception being Fanon, who is quoted selectively and without any reference to his ontological and structural theories. She thus offers an argument for a view (that violence is instrumental, not constitutive) that her opponents would probably not dispute.
The impression left is that Arendt does not understand the kind of structural critique of liberalism/capitalism which New Left authors pursue. She takes a lot for granted in her account, naturalising and glorifying existing institutions, and often seems unable to think outside their boundaries even to the degree necessary to make sense of opposing viewpoints. The real quarrel with the New Left is not so much about violence as about the structural critique of the status quo as systematically oppressive, and the relation of radical antagonism which results from this critique, but Arendt mis-perceives it as a dispute about violence, reconstructing her opponents' views by cross-reading their conclusions with her own assumptions and then arguing against what she assumes their view must be.
The crucial distinction between violence and power is very similar to the distinctions made by authors such as Kropotkin, Ward, Buber, Clastres, Guattari, Negri, Holloway and Agamben between the social principle, or creative power, and the political/command/negative principle. The main difference is that Arendt arbitrarily and clumsily tries to annex the liberal-democratic status quo to the former category (despite admitting at various points the importance of problems such as bureaucratisation and police brutality). This requires, of course, that the violence of liberal states be mystified, and Arendt's concepts of authority and power (especially the latter's elision of the distinction between power-over and power-with or -to) serves precisely this purpose. Arendt seeks a revitalised political community based on Ancient Rome (though with this system's slavery, misogyny, expansionist warfare and gladiatorial fixation apparently ignored). The result is an asymmetrical treatment of the violence of the system and its opponents, posing as an argument about violence in general - a "global-local" in Shiva's terms, the particularity of the western state dressed up as universality. The essay is also blatantly Eurocentric and structurally racist, both in its indirect imputation of "human" absolutes from specifically American/European perceptions and epistemologies, and in its explicit attacks on radical black movements.
I'd advise that Clastres' "Archaeology of Violence" offers a more empirically-informed account of the social functions of violence, that readers interested in the New Left should not trust Arendt's account and should instead or also read texts such as Marcuse's "Essay on Liberation" to gain a sense of this movement, and that readers looking for works on non-violence might be better served by Tolstoy, Havel or Starhawk.