Lao-tseu (Laozi)
Follow the Way (Dao) through non-action.
Misconceptions
Laozi wrote the Tao Te Ching on his own, in the 6th c. BC.
That is the tradition, not an established fact. The only account of his life dates from around 94 BC, and its author, Sima Qian, himself hesitates between several figures. The oldest version found (Guodian, c. 300 BC) contains only part of the text, in a different order; the Mawangdui manuscripts (copied before 168 BC) have yet another arrangement and different words. Most scholars think of a text gathered and reworked in the 4th-3rd c. BC. An older core and a sage named Lao Dan remain possible, but nothing can prove it.
Wu wei (non-action) means doing nothing.
The text says the Way "does nothing, and so there is nothing which it does not do". Non-action is acting without forcing, without personal ambition, and above all early: "order should be secured before disorder has begun". Legge in fact translates "doing nothing (with a purpose)".
The butterfly dream is Laozi's.
It is Zhuangzi's (4th c. BC), the other great Daoist classic: "Once Zhuang Zhou dreamt he was a butterfly…". There is neither butterfly nor dream in the Tao Te Ching.
Yin and yang are at the heart of the Tao Te Ching.
The two words appear only once, in chapter 42: "all things carry yin and embrace yang". The text thinks a lot in pairs of opposites (weak and strong, full and empty), but yin-yang theory and the famous black-and-white symbol were developed later. Julien and Legge do not even translate these two words as such.
Non-action is a Daoist idea that Confucius rejected.
Confucius' Analects use the same expression to praise King Shun, who "governed without exertion": he simply watched over himself and sat gravely on his throne. For Confucius this non-action comes from moral example and ritual; for the Daodejing, from giving up ritual. Same word, different meaning.