Hume was an academic skeptic. His philosophy was first given in his 'Treatise of Human Nature', which he later, not long before his death, retracted, in favour of his 'Enquiries concerning Human Understanding' and 'Enquiry concerning the Principles of Morals'. He also wrote an excellent 'Dialogues upon Natural Religion', that was only published after he had died.

He was not the first to see fundamental problems with the notions of induction and causality, but was the first to clearly articulate these and draw public attention to them.

Because Hume was a non-believer he never got an academic position and found many religious detractors. His argument on miracles is an important against many religious arguments. Essentially, it is this: At the very least a miracle must have a very low probability to be a miracle - which means that the probability that such a kind of event in reality did not happen must be as high as the probability that it did happen is low, because, writing M for the supposed miracle, pr(M)+pr(not-M)=1. Therefore it is a near certainty that miracles do not happen, even if they are defined as events that may happen but have very low probability. And it is a certainty there are no miracles if miracles have a zero probability and are impossible. Consequently, it is far more probable in any report or experience of a supposed miracle that one is deceived or receives false evidence.