What does it mean "no first use"? Have NATO applied this concept ? In what ways? Who was the first to develop this concept? What are the work laying the foundation of the concept?
"What does it mean"?
No first use (NFU) refers to a pledge or a policy by a nuclear power not to use nuclear weapons as a means of warfare unless first attacked by an adversary using nuclear weapons. Earlier, the concept had also been applied to chemical and biological warfare.
First use of "No First Use"
Again from Wikipedia:
China became the first nation to propose and pledge NFU policy when it first gained nuclear capabilities in 1964, stating "not to be the first to use nuclear weapons at any time or under any circumstances"
- However, the first use of the term goes as far back as 1946, in Bulletin of the Atomic Scientists, Volume 32 / Atomic Scientists of Chicago, 1946
Have NATO applied this concept?
To answer the question: not in its pure form. Specific use policies and how close they come to "No first use" for both US and UK are elaborated in detail on that same exact Wikipedia page.
Pakistan, Russia, the United Kingdom, the United States, and France say they will use nuclear weapons against either nuclear or non-nuclear states only in the case of invasion or other attack against their territory or against one of their allies. Historically, NATO military strategy, taking into account the numerical superiority of Warsaw Pact conventional forces, assumed that the use of tactical nuclear weapons would have been required in defeating a Soviet invasion.
At the 16th NATO summit in April 1999, Germany proposed that NATO adopt a no-first-use policy, but the proposal was rejected.
For bonus points, even the much-vaunted supposed USSR's temporary NFU policy between 1982 and 1993 may have likely been just a PR stunt:
In June 1982, the Soviet Union undertook a unilateral pledge not to resort to the first use of nuclear weapons. How seriously the Soviet Union regarded this commitment is open to debate. For example, Therese Delpech, of the French Foreign Office, has written that:
...military records of the Warsaw Pact that fell into German hands demonstrated beyond doubt that Russian operational plans called for the use of nuclear and chemical weapons in Germany at the onset of hostilities, even if NATO forces were using only conventional weapons—this at a time when the Russian official doctrine was no first use.
(source: "No First Use of Nuclear Weapons" by Feiverson; citing in turn 'Therese Delpech, “New Stages of Nuclear Disarmament: A European View,” in H.A. Feiveson, editor, The Nuclear Turning Point, (Washington, DC: The Brookings Institution, 1999), p. 335.)')