In a cursory search, I found that there is no set idea of how many branches there are. I’ve seen anywhere from 4 to 16 branches. But among the most common are: Epistemology, Metaphysics, Logic and Ethics. (and Aesthetics, which is the philosophy of art, beauty. It is important because it illustrates the human ability to create abstractly and physically, to represent the world artfully, precisely or to see the world from a new perspective.
Epistemology is the study of knowledge; how we acquire knowledge. Rationalism and Empiricism; what can we learn from reason or just conceptual thinking and what do we learn only from experience.
Metaphysics is not just the study of spiritual or qualitative states above (beyond) the physical. This branch of philosophy is about the nature of ideas, material and immaterial, the nature of phenomena. Included are ontology, reality/actuality, mind, will.
Ethics is the study of morality; good and evil. This is a generalization. Ethics also covers more specific concepts of human compassion and interaction such as forgiveness, charity, justice, altruism/individualism – and from here, ethics can often segue into political philosophy which can be a separate area of philosophy itself.
Logic is the study of argumentation and reason. Closely related to epistemology (how we acquire knowledge), logic is the critical analysis of that knowledge. Mathematic philosophy is included here for its rigorous objectivity. Often, logic is divided into deduction (going from a broad general conclusion to smaller clues) and induction (going from smaller clues to a larger, general deduction).