Hadith Qudsi are the sayings of the Prophet Muhammad as revealed to him by the Almighty Allah.
Hadith Qudsi (or Sacred Hadith) are so named because, unlike the majority of Hadith which are Prophetic Hadith, their authority (Sanad) is traced back not to the Prophet but to the Almighty.

Among the many definitions given by the early scholars to Sacred Hadith is that of as-Sayyid ash-Sharif al-Jurjani (died in 816 A.H.) in his lexicon At-Tarifat where he says: "A Sacred Hadith is, as to the meaning, from Allah the Almighty; as to the wording, it is from the messenger of Allah . It
is that which Allah the Almighty has communicated to His Prophet through revelation or in dream, and he, peace be upon him, has communicated it in his own words. Thus Qur'an is superior to it because, besides being revealed, it is His wording."

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Hadith Qudsi 1:
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On the authority of Abu Hurayrah (may Allah be pleased with him), who said that the Messenger of Allah said:

When Allah decreed the Creation He pledged Himself by writing in His book which is laid down with Him: My mercy prevails over my wrath.

It was related by Muslim (also by al-Bukhari, an-Nasa'i and Ibn Majah).

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Hadith Qudsi 2:
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On the authority of Abu Hurayrah (may Allah be pleased with him), who said that the Messenger of Allah said: Allah Almighty has said:

The son of Adam denied Me and he had no right to do so. And he reviled Me and he had no right to do so. As for his denying Me, it is his saying: He will not remake me as He made me at first (1) - and the initial creation [of him] is no easier for Me than remaking him. As for his reviling Me, it is his saying: Assah has taken to Himself a son, while I am the One, the Everlasting Refuge. I begot not nor was I begotten, and there is none comparable to Me.

(1) i.e., bring me back to life after death.

It was related by al-Bukhari (also by an-Nasa'i).