Short answers, pulled from the story.
Knowledge is most often defined as justified true belief, naming three features: a belief that is true and justified. Knowledge of facts is called propositional knowledge, and there is wide agreement that it is a form of true belief, though justification remains heavily disputed.
Gettier cases are counterexamples formulated by epistemologist Edmund Gettier in the 20th century. They present justified true beliefs that fail to be knowledge because of epistemic luck, as in the case of a driver who stops by chance before the only real barn among many barn facades.
The main split is between propositional knowledge, or knowledge-that, and non-propositional knowledge such as knowledge-how and knowledge by acquaintance. Further distinctions include a priori versus a posteriori knowledge, explicit versus tacit knowledge, and the Eastern divide between higher and lower knowledge.
The main sources of knowledge are perception, introspection, memory, inference, and testimony. Perception is usually identified as the most important source of empirical knowledge, while testimony lets one person know a fact because another talks about it.
Epistemology, also called the theory of knowledge, is the main discipline investigating knowledge. It studies what people know, how they come to know it, what knowledge means, the value of knowledge, and the thesis of philosophical skepticism that questions whether knowledge is possible.
Foundationalism, coherentism, and infinitism are three theories of the structure of knowledge that respond to the threat of an infinite regress of reasons. Foundationalists say some basic reasons end the regress, coherentists say a finite web of beliefs mutually supports itself, and infinitists accept an infinite chain of reasons.
Knowledge may be valued because it is useful, giving it instrumental value, or because it is good in itself, giving it intrinsic value. In Plato's Meno, knowledge is held to be better than true belief because it is more stable, while virtue epistemology locates its extra value in the manifestation of cognitive virtues.