Which branch of philosophy investigates the nature of knowledge and methods of acquiring knowledge?

The branch of philosophy that specifically investigates the nature of knowledge and the methods of acquiring knowledge is epistemology. It explores questions related to belief, justification, and truth, seeking to understand how we know what we know. Epistemology considers various sources of knowledge, such as perception, reason, memory, and testimony, and evaluates their reliability and validity. This field is fundamental in both philosophy and scientific inquiry as it helps to establish the foundations upon which theories and claims are built.

Ontology, while an important branch of philosophy, focuses on the nature of being and existence rather than on knowledge itself. Realism pertains to beliefs about reality and may describe the existence of objects independently of perception, but does not specifically address the acquisition of knowledge. Axiology deals with values and ethics, exploring questions of what is right or good, which is distinct from the epistemological focus on knowledge. The emphasis on acquiring knowledge and understanding its limits makes epistemology the correct choice in this context.