The Examined Life
Socrates wrote nothing. Everything comes through others — Plato, Xenophon, Aristophanes — and they disagree, which is the Socratic problem: separating the historical man from Plato's mouthpiece. The rough consensus is that the early dialogues, which end without conclusions, are closest to him.
His method is the elenchus, or refutation. He asks someone confident to define a term, piety, courage, justice. They offer a definition. He draws consequences from it, together with other things they believe, and shows those beliefs are inconsistent. The definition is abandoned, another offered, and the process repeats. The dialogue characteristically ends in aporia: impasse, with no definition surviving.
This looks purely destructive and is not. The elenchus shows that people who act confidently do not know what they are doing, and Socratic wisdom is exactly the recognition of that. The oracle at Delphi said no one was wiser than Socrates; he concluded, after examining people who claimed knowledge, that he alone knew that he did not know.
Two doctrines are attributed to him. Virtue is knowledge: if you genuinely knew what was good you would do it, so wrongdoing is ignorance rather than weakness. This makes akrasia, acting against one's better judgement, strictly impossible, which is either a deep insight about the nature of knowing or a plain denial of the obvious, and the debate has never closed. And the priority of the soul: caring for one's soul matters more than reputation, wealth or even life, since "it is better to suffer injustice than to do it".
He was tried in 399 BC for impiety and corrupting the youth, and executed. The charges were probably political, several of his associates had been involved in the oligarchic coup, but his defence made things worse: he refused to plead, proposed free meals at public expense as his penalty, and treated the trial as another occasion for examination.
The permanent shift is one of subject: from what the world is made of to how one should live, pursued by argument rather than authority.
Common pitfall: reading Socratic ignorance as false modesty or a debating tactic. He means it. Recognising that you do not know is the only wisdom available, and everything in the method follows, you cannot examine a belief you are certain of.