She was a powerful fucking woman, through her many struggles. She created her own philosophical system, despised both by the left and right. She was a proponent of minarchist capitalism, but primarily of ethics based in egoism. (Egoism and selfishness, here not to be confused with any negative use of these words, such as "egotism" or "egocentrism")
There are many much more controversial, harder to understand and more ambigious quotes one could pull. She also lived quite an extraordinary and often chaotic life.
If you start getting into her ideas at any point, I would recommend staying away from her fiction books and the many left/right wing opinion pieces that have been written on her.