Scepticism, the view that knowledge is impossible, threatens our conception of ourselves as epistemic subjects as much as it endangers our conception of the external world. The book develops a modal account of knowledge and provides an answer to scepticism based on a detailed examination of the main sceptical argument. It discusses prominent contemporary theories of knowledge, in particular safety and sensitivity theories, and shows that they cannot handle Gettier-type examples of a new kind. An alternative analysis of knowledge in terms of relevantly normal possibilities is developed. The sceptical argument addressed aims to show that we cannot know ordinary things because we cannot rule out that we are in a sceptical scenario. Classical responses, like dogmatism, non-closure theories, and epistemic contextualism, are explored and rejected as unnecessary for a refutation of the sceptical argument. A detailed investigation reveals, first, that the failure to know that we are not in a sceptical scenario does not conflict with ordinary knowledge, but only with knowledge that we know, and, second, that we can indeed know that we are not in a sceptical scenario. It is therefore claimed not only that we know, but also that we know that we know.