Free will and determinism
Determinism is the view that every thing that occurs in the world has been fully caused, determined, by prior events and the laws of nature (gravity, thermodynamics, relativity, etc). And this will be true of everything that will occur in the future.
Regarding free will, determinism claims that human thoughts and actions are not exempt. That our every thought and action has been fully caused by prior events and the laws of nature, so this will determine all of our future thoughts and actions. So, this raises the question, if determinism is true, how can we have free will?
Determinists
Those who think that determinism is true, that all of our thoughts and actions are determined by prior events, but also believe that this means we don’t have free will, are called determinists.
Libertarians
Libertarians agree with determinists that if determinism is true, then we don’t have free will. However, they believe that determinism is false. They believe that we are exempt from being determined by prior causes regarding our thoughts and actions.
Compatibilists
Compatibilists agree with determinists that we are are determined by proir causes, but still have free will. That they are compatible with one another. Typically, compatbilists believe that as long as we are doing what we want to do, regardless of whether what we want to do was determined, then we are acting of our free will.
Moral responsibility
The main concern regarding not having free will, is that it is assumed that we can only be held morally responsible for our actions if we did them of our own free will. So, determinists who agree with this would also believe that no one is morally responsible for their actions, whereas libertarians and compatibilists do not have such a worry.
Semicompatibilism
Semicompatibilism is a mixed view that says we don’t have free will because determinism is true, but we can still be held morally responsible for our actions. That having or not having free will is not necessarily needed to hold people morally responsible.
Literature
Below are links for books written defending some of these positions. The first is an argument for determinism by Sam Harris, the second is an argument for compatibilism by Daniel Dennett, and third is an argument for libertarianism by Richard Swinburne.
Sam Harris: https://amzn.to/2ILXWYX
Daniel Dennett: https://amzn.to/2IIeWz8
Richard Swinburne: https://amzn.to/2IGCvbM