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Idealism
Plato is one of the first philosophers to discuss what might be termed Idealism, although his Platonic Idealism is, confusingly, usually referred to as Platonic Realism. https://www.philosophybasics.com/branch_idealism.html -
Realism
Aristotle, a student of Plato who broke with his mentor's idealist philosophy, is called the father of both Realism and the scientific method
https://oregonstate.edu/instruct/ed416/PP2.html -
Pragmatism
Established by Auguste Comte, Charles Darwin and the Americans: Charles Peirce, William James, and John Dewey -
Existentialism
Appeared as a revolt against the mathematical, scientific philosophies that preceded it. -
Neotheism
Established by Thomas Aquinas, this is also known as theistic realism whereby "God exists and can be known through faith and reason" -
Contemporary Philosophies
Present period in the history of Western philosophy beginning at the early 20th century with the increasing professionalization of the discipline and the rise of analytic and continental philosophy.