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After all, Plato and Aristotle are our everything. I am far from a professional in philosophy, but I believe that it is necessary to study from the beginning. Just if you open the same Deleuze or Derrida, you can see that in any case they refer to one of the old men: Hume, Leibniz, Spinoza (Deleuze) and Descartes, Kant, Heidegger (Derrida criticized them all). Looking at existentialism: Sartre retells Husserl, and Husserl is tied to Kant and Descartes (among all the others, of course); Jaspers refers to Nietzsche and Kierkegaard, who in one way or another oppose Hegel, who in turn… Well, you understand.
You can, of course, pick out something from the retellings and aspects of what these authors refer to, but this will not be knowledge and understanding of the ideas of Kant or Spinoza, but their retelling, and somewhere profanity of their ideas. Even if you take someone fresher, like Quentin Meillassoux, he is so deeply tied to Kant and his criticism that you can't do without reading the author of the Critique of Pure Reason himself. You might be able to beat the idea of “After a limb” to smithereens if you read Kant and then scolded Meillassoux in a condescending way: “Oh, Quentin, you don't understand anything.”
It is advisable to read several books in parallel. Most likely, it won't even work out otherwise. The twentieth century, of course, is juicier and seems to be more relevant for us now, but it did not grow up on emptiness, did not arise out of nowhere. Therefore, you can do this: one volume of someone from the old people, the second volume of someone from interesting to you, and a couple of thick textbooks on the history of philosophy and philosophical dictionaries. Well, what can I do? Happiness (and your own monograph) must be endured.
When studying mathematics, should I start with the multiplication table and the Pythagorean theorem? Or is it better to go straight to the works of twentieth-century mathematicians?
If you are not familiar with philosophy, then I recommend that you start learning from the beginning. Because it will be very difficult to understand the thoughts/ideas of 20th-century philosophers without reading the works that were created earlier.