What was Adam Smith's philosophy?
Adam Smith's basic philosophy was the philosophy of laissez faire capitalism. That is, he felt that the government should not interfere in the functioning of the market place.
Adam Smith believed that a market that was left to itself would be the most efficient in creating all the things that people wanted at the lowest possible prices. He believed that people, trying only to fulfill their best interests, would create a system that would be best for everyone. This was his concept of the best possible economy being created by the "invisible hand."
Smith also believed in free trade. He was strongly opposed to the mercantilist ideas of his time. This was, he felt, another form of government intervention. Free trade would, he thought, bring more prosperity to everyone involved.
Adam Smith was a Scottish moral and political economy philosopher. In moral philosophy Smith sought to understand human feelings especially with regards to sympathy and virtues. He states that virtues emanate from a person's ability to adjust their feelings to reflect what others are feeling, or in other words the attempt to place oneself in other people's circumstances. He came to the conclusion that by impartially sympathizing with others one morally approves of what is felt by others. He went further to establish two guides (rules and virtues) to action as they relate to morality.
Moral rules are the rules that guide societies and help them survive. They offer guidance to everyone within the society including people who are not fully virtuous to at least behave decently, for example when people say “I’ll never do that”, such statements point to social expectations.
Moral virtues on the other hand do not need the rules to be established. Instead they are developed to a point that one does not need any rules to lead a virtuous life.
Philosophy with regards to political economy has been discussed by Pohnpei397 as above.