Before you set out to know anything else with certainty you must first know somethings, on some level, about your own mind and how it obtains information; how to establish certainty and obtain knowledge. The philosopher Ayn Rand defined Epistemology, in her groundbreaking book on the subject, as “a science devoted to the discovery of the proper methods of acquiring and validating knowledge.” This is the most fundamental branch of philosophy from the perspective of the obtainment of knowledge.
To discover the facts of reality you must also know somethings, on some level, about the basic nature of reality. The science that studies this sets the terms for all other sciences, including epistemology, and all other knowledge. Metaphysics is fundamental from a different perspective in that reality would still exist if there were no consciousness to perceive it. The basic facts of reality are understood implicitly before you can understand how to learn any facts. Once you grasp some method of discovering facts you can then turn that method on this implicitly understood information and make your understanding of it explicit.
Once you have established what kind of world you live in and what kind of entity you are you can then consider how you should act and why. The how is the science of ethics, the why is meta-ethics. Ethics gives us a set of principles to guild our actions. Meta-ethics explains why we need a code of values and how we can establish one by the proper method of acquiring any knowledge. Politics is an application of ethical principles on a social scale. It defines the purpose of a government and explores a proper government’s limitations and sets the terms for the actions it may take. It also deals with such questions as why a government is needed at all.
Based also on ethics, epistemology and, more than either of these, metaphysics is the science that studies the nature of art and the standards by which to judge it. The broader of the two branches of philosophy which depend on the three more basic branches is aesthetics.
These are the five branches of philosophy.