She wrote four novels ("We the Living", "Anthem", "The Fountainhead", and her 1100-page book "Atlas Shrugged") and many other essays and nonfiction works in which she explains and explores her dubious philosophy, which she named "Objectivism". She used a capital "O" to distinguish her philosophy from objectivism with a lowercase "o", which predates Rand and is simply a belief in an objective, rather than a subjective, reality. While Rand's Objectivism encompasses classic objectivism, it is a vast monolith, trying to address areas such as economics and politics.
Ayn Rand was the one of the few recent philosophers who
believed in objective reality believed her subjective view had to be objective reality, she also believed in the power of human reason to deduce anything to arbitrary precision her personal capacity to deduce anything to arbitrary precision. This led her to reject Gödel, non-Euclidean geometry, quantum physics, and relativity). She rejected also the notion that human beings cannot know anything with certainty and imagined that she was closer to the truth than Albert Einstein, Niels Bohr, Werner Heisenberg and other highly intelligent, respected scientists who developed the Uncertainty principle. And physical science wasn't even her main field of study, mainly she studied economics and social science. She rejected the historical determinism of Marxism which suggests that human beings are incapable of controlling their own destinies but felt instead that her objectivism should control human destiny. She was also utterly conceited in imagining her interpretation of libertarianism was the only truth, this she believed encompasses laissez-faire capitalism most of all.
Ayn Rand's philosphy, which she named "Objectivism" (as distinguished from objectivism with a lowercase "o", which predates Rand and is simply a belief in an objective, rather than a subjective, reality) can be divided into four main parts:
Metaphysics: Objective Reality (There is a real world which exists independent of our senses.) Most of us believe this intuitively though it can’t be proved.
Epistemology: Reason (The only way to determine the truth of a statement is by the use of reason; faith gives us no certain knowledge whatever. Note that she believed this could be used to absolute precision to determine any truth.) Ayn Rand believed that all human beings using reason should reach identical conclusions, naturally she believed the conclusions she had reached were the correct conclusions and those who disagreed with her weren't using reason properly. The followers of Ayn Rand accept Rand's conclusions as a matter of faith but probably don't realize this is a faith position.
Ethics: "Rational Self-interest" (Rand saw ethics as predetermined and absolutist, divided into absolute egoism and absolute altruism--in the Comtean sense--and saw altruism as a moral cannibalism in which the individual is sacrificed for the good of the group). She saw absolute selfishness as the highest virtue.
We don't fear Rand because she's dead but we fear her teachings.