This is just a quick outline of the philosophers mentioned in the book and their general ideas—it is in no way comprehensive.
Socrates (470 - 399 BC): Humans posses basic intellectual and philosophical virtues, those are the most valuable things and should be explored. Laid groundwork for logic/reasoning.
Democritus (460 - 370 BC): World made out of atoms, little indivisible units.
Plato (428? to 348? BC): Searching for the "Platonic Ideal"—there is some form (like a cookie cutter) above everything else, like a perfect horse, and everything else is a shadow of that.
Plato's Cave: imagine there is a light shining outside a cave. We are only able to see the shadows of the ideal forms that are cast on the wall.
Aristotle (384 - 322 BC): Empiricism above all, only trust what your eyes can see, that is somethings truest form.
Cynics (450 BC): Casting away others opinions and society brings you true freedom.
Stoics (300 BC): Monism—"a theory or doctrine that denies the existence of a distinction or duality in some sphere, such as that between matter and mind, or God and the world." All things that happen are natural, you should learn to handle it.
Epicureans (307 BC): The highest good is pleasure, the greatest evil pain. The focused on avoiding pain, vs enduring it like the Stoics. Cousin of hedonism.
Augustine of Hippo (354 - 430): Everything God creates is good, and all evil is the result of straying from God's path.
Thomas Aquinas (1225 - 1274): Scholasticism—combination of religious thought and philosophy. Logic wasn't in opposition with faith, in fact it was the opposite, and we could use logic to prove the existence of, and get closer to, God
Rene Descartes (1596 - 1650): Rationalism: logic is the highest form of thought. "I think therefore I am". Really liked proofs.
David Hume (1711 - 1776): Empiricism, opposite of Descartes. Anything real has to come from experience. Rejected the idea that humans were created in the image of God.
John Locke (1632 - 1704): Opposite of Hobbes, believed that humans have inherent rights, (life, liberty and property), and should overthrow their rulers if their rights are being violated. Large influence on concept of democracy.
There was a contrast during the time between continental rationalism and English empiricism.
Baruch Spinoza (1632 - 1677): Philosophy is like a religion. Was an atheist, which was very rare during the time. Nature and God were one.
Immanuel Kant (1724 - 1804): Morality comes from reason not emotion—it's about your intentions, not the results. To act morally, you have to act with the correct intentions.
Georg Hegel (1770 - 1831): History could be understood and it progressed in a rational way.
Søren Kirkegaard (1813 - 1855): It was important to just live life and think about what matters to you—what's the point of studying philosophy that doesn't concern your life.
Karl Marx (1818 - 1883): History had 5 stages, ultimately ending up with communism where workers own means of production. Worked with Friedrich Engels.
Sigmund Freud (1856 - 1939) Ego: rational decision making, balances pleasure with reality. Id: animal-like, wants immediate pleasure. Superego: learned rules and norms, tries to suppress the Id.
Charles Darwin (1809 - 1882): Evolution...
Albert Camus (1913 - 1960): We should embrace the absurdity of being human.
Jean-Paul Sartre (1905 - 1980): Existentialism, we can be pressured into "bad faith" where society forces us to do things we don't want and get rid of our freedom. No grater design or purpose.
Simone de Beauvoir (1908 - 1986): Pioneer of modern feminism, existentialist, source of women's oppression is societal and historical, not innate.