Laozi (Lao Tzu), answered from the texts and cited to the page.
Wu wei (無為, non-coercive action) is not literal non-action or passivity. It is acting without imposing on the natural unfolding of things, acting in accordance with ziran (自然, the so-of-itself, the spontaneous patterns of the ten thousand things). The two concepts are paired and inseparable: ziran is the descriptive metaphysical claim that the ten thousand things have their own spontaneous patterns of arising and flourishing; wu wei is the prescriptive practical-political- cultivational claim that one should not interfere with those patterns.
Ch. 37 states the core principle: the Dao constantly does nothing, yet nothing is left undone. The Dao does not act in the sense of coercive intervention; the ten thousand things flourish through their own ziran; the result is that everything is accomplished without action. Ch. 48 articulates the cultivational path: in the pursuit of learning, every day something is gained; in the pursuit of the Dao, every day something is dropped; less and less, until non-action is reached; do nothing and nothing is left undone.
The sage's practice is the progressive shedding of coercive intent, the alignment with the spontaneous patterns, the action that does not act. Ch. 57 applies this to governance: I take no action and the people of themselves are transformed. The political and personal practice flows from the metaphysics of ziran; the metaphysics is what makes the practice intelligible.123
The work is done, but how no one can see; 'Tis this that makes the power not cease to be. 3. 1. Not to value and employ men of superior ability is the way to keep the people from rivalry among themselves; not to prize articles which are difficult to procure is the way to keep them from becoming thieves; not to show them what is likely to excite their desires is the way to keep their minds from disorder. 2.Tao Te Ching
When there is this abstinence from action, good order is universal. 4. 1. The Tao is (like) the emptiness of a vessel; and in our employment of it we must be on our guard against all fulness. How deep and unfathomable it is, as if it were the Honoured Ancestor of all things! 2.Tao Te Ching
This is the reason why all under heaven consider it the most valuable thing. 63. 1. (It is the way of the Tao) to act without (thinking of) acting; to conduct affairs without (feeling the) trouble of them; to taste without discerning any flavour; to consider what is small as great, and a few as many; and to recompense injury with kindness. 2.Tao Te Ching
Wu wei is one of the most-studied concepts in early Chinese philosophy and one of the principal vehicles for the contemporary comparative-philosophical engagement with the Daodejing. Edward Slingerland's Effortless Action (Oxford UP, 2003) is the principal contemporary scholarly treatment, tracing the wu wei concept across early Chinese thought (Confucian, Daoist, and other) and identifying the "paradox of wu wei" (how does one try to be not-trying?) as a productive tension. Moeller's Philosophy of the Daodejing treats wu wei through the system-theoretical lens as the non-interfering action that lets spontaneous order self-organize. Liu Ch. 4 provides the principal textual-analytic modern treatment of the ziran-wu wei pairing. The Zhuangzi develops the wu wei doctrine substantially (Liu Part II); the relationship between Laozi's and Zhuangzi's wu wei is an ongoing scholarly question.