I know many sneer at the idea of Ayn Rand as a philosopher. (Just look at reviews below.) I believe mainly because they're so radically opposed to her views and so consider her a threat to their values. And many find it easy to be derogatory because she won fame as a writer of fiction and didn't have the academic credentials of those who usually call themselves philosophers. And sorry to say, it probably didn't help back then--may even hurt her now--that she was a woman poaching on very male territory. All I can tell you is that the much-lauded Anarchy, State and Utopia by Robert Nozick, which won a National Book Award in philosophy and religion, basically takes Ayn Rand's political arguments and presents them in academic language and is by someone with those academic credentials--and it's awarded respect.
But if any aspect of her philosophy has some grudging acknowledgement from philosophers, and is truly original, it's probably her epistemology. Epistemology is that branch of philosophy that deals with knowledge--its nature, what can we know, how do we know it. Once, when Ayn Rand was asked to define her philosophy while standing on one foot, she replied: "Metaphysics: Objective Reality; Epistemology: Reason; Ethics: Self-Interest, Politics: Capitalism." Well, I might take issue with "capitalism" as the name of a political, rather than economic concept, but otherwise that's summarizes her beliefs well. But then a lot of philosophers might define themselves similarly. What makes a philosophical system are the details and the arguments. In the case of epistemology this book actually has a pretty narrow focus--though a crucial one. The original edition was not much longer than 100 pages--a very slim mass paperback. Peikoff has added to it material from taped lectures. Basically, this focuses on the nature of concepts and especially concept formation and how that feeds into consciousness and identity.
These are difficult concepts--within any philosophy. Just try reading Locke or Kant on the subject. In this Rand's lack of an academic background and her strengths as a popularizer of philosophy is a blessing: because the arguments she presents are lucid and clear. You can find the main criticisms of the arguments on the Wiki--that it doesn't take cognitive psychology into account and that "conflates the perceptual process by which judgments are formed with the way in which they are to be justified." I haven't read the counterarguments in their entirely in a way I can judge their validity. But personally, and I know this is not in itself an argument for her epistemology--but I know how relieved I felt to find a thinker defending the validity of the senses and reason after I had been filled with philosophers in school that would deny their reality. So yes, I find this book amazing, powerful and valuable.
