Steven Lukes's Power: A Radical View was a very important contribution when it appeared in 1974. Lukes emphasized several important points that became landmarks in subsequent discussions of the social reality of power: that power is a multi-dimensional social factor, that power and democracy are paradoxically related, and that there are very important non-coercive sources of power in modern society. In the second edition in 2005 he left the 1974 essay unchanged, but added a substantive introduction and two new chapters: "Power, Freedom and Reason" and "Three-Dimensional Power". Also new in the second edition is substantially more attention to several other writers on the social context of power, including James Scott and Michel Foucault.
Lukes offers a generic definition of power along these lines:
I have defined the concept of power by saying that A exercises power over B when A affects B in a manner contrary to B's interests. (37)But this definition is too generic, and Lukes attempts to provide a more satisfactory interpretation by constructing a "three-dimensional" account of power.
What are the "dimensions" of power to which Lukes refers? He begins his account with the treatment of power provided by the pluralist tradition of American democratic theory, including especially Robert Dahl in 1957 in "The Concept of Power" (link). This is the one-dimensional view: power is a behavioral attribute that applies to individuals to the extent that they are able to modify the behavior of other individuals within a decision-making process. The person with the power in a situation is the person who prevails in the decision-making process (18).
Thus I conclude that this first, one-dimensional, view of power involves a focus on behaviour in the making of decisions on issues over which there is an observable conflict of (subjective) interests, seen as expressing policy preferences, revealed by political participation. (19)The second dimension that Lukes discusses was brought forward in rebuttal to this pluralist theory; critics pointed out that it is possible to influence decisions by shaping the agenda, not merely by weighing in on existing decision points. Lukes quotes from Peter Bachrach and Morton Baratz in their 1962 "Two Faces of Power" (link): "'to the extent that a person or group -- consciously or unconsciously -- creates or reinforces barriers to the public airing of policy conflicts, that person or group has power'" (20). So shaping the agenda is an important source of power that is overlooked in the pluralist model, the one-dimensional view.
The three-dimensional theory of power turns to a different problem -- the fact that people sometimes act willingly in ways that appear contrary to their most basic interests. So the third dimension is the set of ways in which the powerful transform the powerless in such a way that the latter behave as the former wish -- without coercion or forcible constraint -- for example, by creating a pervasive system of ideology or false consciousness. Both pluralists and their critics overlook an important point, in Lukes's view:
The trouble seems to be that both Bachrach and Baratz and the pluralists suppose that because power, as they conceptualize it, only shows up in cases of actual conflict, it follows that actual conflict is necessary to power. But this is to ignore the crucial point that the most effective and insidious use of power is to prevent such conflict from arising in the first place. (27)And again:
What one may have here is a latent conflict, which consists in a contradiction between the interests of those exercising power and the real interests of those they exclude. These latter may not express or even be conscious of their interests, but ... the identification of those interests ultimately always rests on empirically supportable and refutable hypotheses. (28-29)When Lukes returns to the three-dimensional theory in the final essay in the second edition, he shifts the language slightly to refer to "power as domination." Domination can occur through explicit coercive means, but it can also occur through unconscious mechanisms. This allows Lukes to address the theories of people like James Scott (Domination and the Arts of Resistance: Hidden Transcripts) and Michel Foucault (The History of Sexuality, Vol. 1: An Introduction).
In hindsight, it seems a little dubious to refer to these as "dimensions" of power, rather than aspects or forms of power. To call them "dimensions" somehow suggests that overall power is a vector of quantities in three or more orthogonal dimensions, each of which can vary independently. The features that Lukes identifies as "dimensions" seem more like tools in a toolkit or strategies in a repertoire: exercise control by doing X or Y or Z. So the language of dimensions seems inappropriate in this context.
But here is a more basic concern that is visible with the advantage of hindsight: there is very little in Lukes's treatment that sheds light on the social mechanisms of power. What are the social features that enable one individual or group to wield influence in any of these ways? Through what sorts of institutional and individual facts are individuals enabled to exercise power over others? Lukes doesn't address this question; and yet it seems to be the heart of the matter. We would like to have a way of analyzing social relations that allows us to discern how it is that some groups gain the material and social resources necessary to prevail. Marxism offers one such theory -- power derives from class position; but this answer doesn't really satisfy in the contemporary social world. (Lukes devotes a few paragraphs to the debate between Nicos Poulantzas and Ralph Miliband on the right way of understanding the exercise of power within a capitalist society; 54-58.) But generally, it seems fair to say that Lukes comes closer to offering a semantic analysis of the use of the term "power" rather than offering a sociological analysis of the causal and structural reality of power.