Epistemology is the study of knowledge and those things closely related to it: justification, what it takes for you to be justified, the relation between knowledge and justification, whether you can have any justified beliefs at all, and if so, how you come to know (or justifiably believe) things, how you can use what you know (or justifiably believe) to come to know (or justifiably believe) other things, and the value of knowledge.
The literature on epistemology is vast. Here's a very brief summary of some epistemological discussions. Concerning knowledge, many epistemologists think knowledge is justified true belief, where the justification you have is linked to the truth of the matter in the right kind of way, though what this way is a matter of debate; some epistemologists think knowledge can't be analyzed this way. Concerning justification's relation to knowledge, some epistemologists think we don't need to be justified to know, and some think we do need to be. Concerning what it takes to be justified, some epistemologists think that what it takes for you to be justified are only factors internal to the believer (Internalists). Others think it takes an external factor, like reliable or well-functioning cognitive faculties (Externalists). Concerning justification, epistemologists differ on whether in any case you there is only one doxastic attitude you are justified in adopting toward a proposition, or whether in some cases more than one doxastic attitude is permissible (as Permissivists maintain). Closely related to the question of “permissivism,” is the question of peer disagreement. Some epistemologists argue that in the face of peer disagreement, one is justified in sticking to one’s guns (as the Steadfast View maintains); others argue that one ought to be conciliatory, moving in the direction of the peer with whom one disagrees (as Conciliationists maintain). Skeptics argue that we can't have any justified beliefs at all, and many epistemologists reply to the skeptic's arguments. Concerning how we use what we know (justifiably believe) to come to know (justifiably believe) other things, some epistemologists (Foundationalists) argue that there are bedrock propositions that we know (justifiably believe), and we build our knowledge (justified beliefs) on those. Foundationalists often take perception, introspection and rational intuition as sources of foundational knowledge, in contrast to testimony (the role of memory being a matter of persistent dispute). Other epistemologists (Coherentists) argue that there aren't bedrock propositions; rather, a set of beliefs is justified as a whole, and several beliefs can be mutually supporting. Concerning the value of knowledge, some argue that knowledge is intrinsically valuable. Others have argued that knowledge is valuable because of the role it plays in practical reasoning, and others argue that knowledge isn't more valuable than justified and true belief, but there are other epistemic states such as understanding, that do have value above their proper subparts. If knowledge is valuable, then treating genuine knowers as if they did not know or depriving people of knowledge, for instance because they belong to an outgroup, can be a form of epistemic injustice.
For an argument that knowledge requires more than justified true belief, see Gettier 1963. For a view that knowledge can't be analyzed in the traditional (justified and true, non-Gettiered belief) way, see Williamson 2000. For a view that knowledge doesn't require justification, see Goldman 1967, Armstrong 1973, and Nozick 1981. For a defense of skepticism, see Unger 1975, and for replies to skeptical arguments, see Sosa 2007, Conee & Feldman 2004, and DeRose 1995. For a defense of internalism, see Chisholm 1966 and Conee & Feldman 2004. For a defense of externalism, see Alston 1989, Goldman 1999, and Kornblith 2001. For a defense of permissivism, see Schoenfield 2014 (and for criticisms, see White 2005). For a defense of the steadfast view of peer disagreement, see Kelly 2005, and of the conciliationist view, see Christensen 2007. For overviews of the epistemology of perception, see Siegel & Silins 2015; of introspection, see Gertler 2015; of rational intuition, see Casullo 2003; of testimony, see Lackey 2008; and of memory, see Huemer 1999. For a defense of foundationalism, see BonJour & Sosa 2003 and Pryor 2005. For a defense of coherentism, see BonJour 1985 and Lehrer 1990. For the view that knowledge plays an important role in practical reasoning, see Hawthorne 2004, Stanley 2005, and Fantl & McGrath 2009 (and for criticisms, see Brown 2008). For discussions of the value of knowledge, see Kvanvig 2003, Haddock et al 2009 and Zagzebski 2003. For discussions of epistemic injustice, see Fricker 2007, Mills 2007, and Medina 2012.
Introductory books: Audi 1997, BonJour 2009, Feldman 2003, Nagel 2014, and Pritchard 2006. More advanced introductions: Goldman & McGrath 2014 and Sosa 2017. Anthologies: Huemer 2002 and Kim et al 2008. Handbooks: Bernecker & Pritchard 2010, Dancy et al 2010, and Moser 2002.