You have quite a large question being asked to try to answer in such a small format; however, I will give you a quick "crash course."
Philosophy is usually divided in one of three ways---chronologically, geographically, or topically. Of the three, the first and third are probably the more commonly known divisions.
Dividing philosophy CHRONOLOGICALLY. This can be done numerous ways, but it is often done with "frames" such as Ancient, Medieval, Modern, and Contemporary. For example, Socrates, Plato, and Aristotle would fall under Ancient while Hume, Descartes, and Leibniz would be in Modern. This gets even more complicated by the fact that what we would call "Contemporary" in this "frame" really has two branches: (1) Analytical philosophy and (2) Continental philosophy. In Analytical philosophy, one is looking usually at things like the philosophy of science and formalistic logic; conversely, Continental philosophy is not easily defined because it can cover everything from phenomenology (Husserl), existentialism (Sartre), linguistics (Saussure), and power (Foucault) to postmodernity (Lyotard) and feminism (Irigaray).
Dividing philosophy GEOGRAPHICALLY. This is usually simply done via the East/West divide established by British imperialism. Eastern philosophy includes Shintoism, Buddhism, Hinduism, Sufism, Taoism, etc. In contrast, Western philosophy is what most people think of when they think of philosophy and what the previous category of chronology was framing. Sometimes, there are colleges courses in British philosophy (eg., Mill and Benthem), American pragmatism (Dewey), French philosophy (Derrida), etc.
Dividing philosophy TOPICALLY. The word "topically" doesn't really fit; it may be better to call it categorically, but each of these are really "subsets" within philosophy. Yet, any statement has any of these within it.
Metaphysics--what is the fundamental nature of reality?
Ontology--what is being? Or what is Being?
Epistemology--what counts as knowledge? How does one know when he/she has knowledge?
Ethics--what counts as "right" action?
Aesthetics--what counts as beauty?
As for famous philosophers, you have to say that from the Western perspective Plato is huge. The philosopher Whitehead even said, "Every work of philosophy is but a footnote to Plato" because Plato was so significant. In the Modern period, Descartes gets a ton of attention due to his "cogito ergo sum" (I think, therefore I am) assertion, which was an epistemological attempt at seeking certainty. In more recent times, I am a fan of both Wittgenstein and Derrida but there is huge debate over contemporary philosophers and their significance, so I will leave you to look into that realm more and make a judgment.
Philosophy is usually divided in one of three ways---chronologically, geographically, or topically. Of the three, the first and third are probably the more commonly known divisions.
Dividing philosophy CHRONOLOGICALLY. This can be done numerous ways, but it is often done with "frames" such as Ancient, Medieval, Modern, and Contemporary. For example, Socrates, Plato, and Aristotle would fall under Ancient while Hume, Descartes, and Leibniz would be in Modern. This gets even more complicated by the fact that what we would call "Contemporary" in this "frame" really has two branches: (1) Analytical philosophy and (2) Continental philosophy. In Analytical philosophy, one is looking usually at things like the philosophy of science and formalistic logic; conversely, Continental philosophy is not easily defined because it can cover everything from phenomenology (Husserl), existentialism (Sartre), linguistics (Saussure), and power (Foucault) to postmodernity (Lyotard) and feminism (Irigaray).
Dividing philosophy GEOGRAPHICALLY. This is usually simply done via the East/West divide established by British imperialism. Eastern philosophy includes Shintoism, Buddhism, Hinduism, Sufism, Taoism, etc. In contrast, Western philosophy is what most people think of when they think of philosophy and what the previous category of chronology was framing. Sometimes, there are colleges courses in British philosophy (eg., Mill and Benthem), American pragmatism (Dewey), French philosophy (Derrida), etc.
Dividing philosophy TOPICALLY. The word "topically" doesn't really fit; it may be better to call it categorically, but each of these are really "subsets" within philosophy. Yet, any statement has any of these within it.
Metaphysics--what is the fundamental nature of reality?
Ontology--what is being? Or what is Being?
Epistemology--what counts as knowledge? How does one know when he/she has knowledge?
Ethics--what counts as "right" action?
Aesthetics--what counts as beauty?
As for famous philosophers, you have to say that from the Western perspective Plato is huge. The philosopher Whitehead even said, "Every work of philosophy is but a footnote to Plato" because Plato was so significant. In the Modern period, Descartes gets a ton of attention due to his "cogito ergo sum" (I think, therefore I am) assertion, which was an epistemological attempt at seeking certainty. In more recent times, I am a fan of both Wittgenstein and Derrida but there is huge debate over contemporary philosophers and their significance, so I will leave you to look into that realm more and make a judgment.
