2010 amendments added to original 2003 review --
As noted by other reviewers, this reading of Hegel is a post-Nietzsche, post-Marx, post-Heidegger reading. By this I mean that Kojeve recognizes the importance of these post-Hegel threads of thought, and attempts to incorporate their best points, just as Hegel would have. It is therefore scorned by some Hegel 'purists' like Mr. Trejo below.
Having read quite a few commentaries on, and interpretations of, the Phenomenology, I would say that this one is the most well-written, in the sense that it illuminates some very difficult Hegelian concepts (like "Spirit" itself) in a searingly direct manner. When one reads Kojeve, there is no doubt that difficult or ambiguous passages are not products of gratuitous showing off or self-indulgent excursions (as one encounters in writers like Derrida and his children) but rather reflect the genuine difficulty of the subject matter the author is trying to articulate. Also, I have read no other writer so convincing in their argument as to Hegel's basic rightness in his grasp and description of "the concept " (the concept of concepts) which brings closure to the riddle of Western metaphysical thought.
I would agree with the 'purists' in not taking this book as the 'definitive' interpretation of Hegel -- it can't excuse not reading Hegel in the original, or other commentaries -- but I would call it essential within the spectrum of Hegelian thought.
This book shows Hegel, though famously critical of Kant, to be essentially the extender of the Kantian philosophy to it's own logical conclusion: the completion of the concept of experience, identified as time itself (zeitgeist). That is, human time, identified as departing from nature at the emergence of specifically human desires, i.e. desire for recognition, desire for the symbolic. This 'absolute subject' of human existence, in transcendental terms, constructs itself rationally by self-reflection on its own object-negating, nature-negating, given-negating activity or creativity. Humanity invents the system of clock time after reflecting on our own ability to temporally transform the given, and so to measure a 'progress': to count state B, following some transformative labor, as a better state of being than state A which preceded that effort. This immanently made conception of time is categorically different than the classical notion of a rational time that would exist somehow outside or independently of thought -- for Hegel the latter idea is the illusion of a confused thinker.
Kojeve's reading however, though convincing in it's demonstration of an anthropologically necessary historical development toward Hegelian 'harmony' between (acting) subject and (being) object, leaves out Hegel's attempt at the 'absolute identity' of the object. This can be read in two ways that Kojeve touches on. First, in the rationalistic, idealistic sense that the object is necessarily different from the subject to ensure the ability of a subject to realize itself as a self, as a free subject of object-negating, creative, activity. Another way to read this is as simply Kojeve's dismissal of Hegel's 'merely aesthetic' Philosophy of Nature and it's more cosmic attempt at spiritualizing the notion of matter.
Commentators such as Stephen Houlgate seem to represent the idealistic view that in absolute knowing nature comes to be fully intelligible to and 'within' spirit. But other recent commentators, such as Joseph Flay and Ardis Collins, are in my view more sober, more realistic, and more likely to persuade mainstream thought in the Anglo-American world to recognize Hegel's vital insights. In their view, nature retains an independence and even resistance to the rationality of the concept, even for what Hegel calls absolute knowing. The perennial problem of induction (sometimes called Hume's problem) in the philosophy of (natural) science testifies to this seemingly intrinsic resistance of nature to the kind of rationality we 'in spirit' are capable of conceiving.
Kojeve's dismissal of 'absolute idealism' (did Hegel even use this term?) can also be understood as the Heidegger-influenced side of his reading. Most contemporary Continental thought is in agreement here that the absolute idealist reading of Hegel does not metaphysically supersede Kant's conclusion in his 3rd Critique that philosophy consists in an irreducibly Aesthetic relation between the concept and the singularity of that-which-resists total rationalization (i.e. nature).
Yet this should not be understood to imply failure by Hegel, rather, it should point us to Hegel's true accomplishments: (1) delivering tremendously relevant insights regarding the concrete, material history of mankind and human experience, by wrestling formidably with Kant's brilliant but very bare, formalistic framework, the critical philosophy of reason itself; (2) rendering the whole historical evolution of Western thought more intelligible than it had ever been prior, and thereby giving us enough intellectual satisfaction to finally drop many inherited but fruitless metaphysical problems.
My own tentative conclusion is that Hegel, along with the existentialist and phenomenological thinkers following him (including Kojeve), can be understood as essentially philosophers of the subject in the Western tradition. While greatly illuminating the conditions, formation, and character of human self-hood, they also force us to feel the limits of self-reflection. Thus they arouse in us who are philosophical, introverted types, the sense that we must also take partisan, decisive actions in the world beyond contemplation.
2011 update: Contra Kojeve: a revised view of Hegel's Philosophy of Nature and contention that "the Real is Rational"
Instead of revising what I've already written above and thus what others have actually rated, I'm adding this revision separately. My view on Hegel's philosophy of nature has changed, and I do now believe that his contention that "the real is rational, and the rational is real" can be reasonably defended. Let me explain how as simply as I can:
Does Hegel ever claim that nature is completely rational? No. Does Hegel recognize that the natural scientist is never going to find that his inductions from observation of nature conform to precise deductive logic? Yes. In a way, the fact that natural science cannot be deductive is actually supportive of Hegel's central insight about nature: nature is only rationality in germ, not developed or become self-reflective as in human discourse. What does it mean to say that nature is only rationality in germ? If the essence of reason is the relation of identity-in-difference, and if nature shows itself most basically in the temporal movement of patterns, repetitions, reproductions, and resemblances -- i.e. not in any simply eternal or 'present' stuff, but in temporal patterns, repetitions, reproductions -- then we can affirm that such patterns are only the habitual or natural form of what has the potential to become self-realized in cognition: reason. Reason in this sense also becomes the self-grasping ability To Differ from the merely given patterns of nature. And this ability-to-Differ or Difference-in-itself is another way of naming the cognitive achievement of absolute spirit.