The Merriam-Webster Dictionary defines individualism as the concept that all duties, values, and rights are derived from individuals rather than a group. Individualism expresses the idea that the needs and rights of the individual are of supreme importance.
With that definition in mind, we can clearly see how Robinson Crusoe expresses individualism. Crusoe, stranded all alone on a deserted island, is necessarily left to his own resources and has to make his own practical and ethical decisions. Though he is lonely in his new home, he forges onward and does what he needs to do to survive. When he does realize he is thriving in his new home, he is proud of his individualism and independence. Further, he does not perceive the land and resources of the island as a shared resource but as his own domain. He, individually, is owner of his island. As he writes:
I descended a little on the side of that delicious vale, surveying it with a secret kind of pleasure, though mixed with my other afflicting thoughts, to think that this was all my own; that I was king and lord of all this country indefensibly, and had a right of possession; and if I could convey it, I might have it in inheritance as completely as any lord of a manor in England.
The arrival of Friday does not lead to equality or mutual exchange but to Crusoe asserting and imposing his individual values and using Friday for his own needs.
Individualism is shown most strongly by Robinson Crusoe himself, who acts to keep himself alive without help for a long time. Since he is the only survivor of his shipwreck, there is no one to help him in the first months of his solitude. Refusing to give up, Crusoe begins to build a shelter out of debris even before the wrecked ship floats closer to shore. Once he has access to tools and better supplies (such as tarp canvas from the ship's sails) Crusoe begins to create an entire household for himself, including farmlands and domestic animals. Although he comes to a religious conversion, he does not give over his personal responsibility, instead thanking God for helping him while still working to help himself. In this fashion, his individualism comes into full force because of his trials, and is the primary factor in his continuing survival and success.