Allah speaks of His Mercy in numerous places in the Quran.

1) “My Mercy embraces all things” [Quran 7/156]

2) “Say (O Muhammad-PBUH) To whom belongs all that is in the heavens and the earth?” Say: “To Allah. He has prescribed Mercy for Himself.”[Quran 6/12]

3) “When those who believe in Our Ayat (proofs, evidence, verses, lessons, signs, revelations, etc.) come to you, say: “Salamun ‘Alaikum” (peace be on you); your Lord has written (prescribed) Mercy for Himself, so that if any of you does evil in ignorance, and thereafter repents and does righteous good deeds (by obeying Allah), then surely, He is Oft-Forgiving, Most Merciful.” [Quran 6/54]

4) Quran has 114 Chapters you will find the phrase “ In the Name of Allah, the Most Gracious, the Most Merciful”

5) “Say (O Muhammad-PBUH) “Invoke Allah or invoke the Most Gracious (Allah), by whatever name you invoke Him (it is the same), for to Him belong the Best Names.”[Quran 17/110 ]

6) “Say: “O ‘Ibadi (My slaves) who have transgressed against themselves (by committing evil deeds and sins)! Despair not of the Mercy of Allah: verily, Allah forgives all sins. Truly He is Oft-Forgiving, Most Merciful.” [Quran 39/53]

7) “And the servants of the Most Merciful are those who walk upon the earth easily, and when the ignorant address them [harshly], they say [words of] peace(safety,” i.e., words free from fault or evil.)” [Quran Surah Al-Furqan 25/63]

8) “Do not commit mischief on the earth after it has been set in order, and call on Him (Allah in prayer) with fear and hope (longing desire): “for the Mercy of Allah is always near to those who do good.” [Quran Surah Al-A’raf 7/56]

9) “And whoever does evil or wrongs himself but afterward seeks Allah’s Forgiveness, he will find Allah Oft-Forgiving, Most Merciful.”[Quran 4/110]

The mercy of Allah manifests itself in His overlooking the sins of the sinner when he unknowingly commits the sin and then repents. Allah’s mercy is even beyond that; Allah changes the sins of the sinner, after his sincere repentance followed by righteous deeds, to good deeds (hasanat). Allah says

10) “Except those who repent and believe (in Islamic Monotheism) and do righteous deeds; for those, Allah will change their sins into good deeds, and Allah is Oft-Forgiving, Most Merciful.”[Quran 25/70]

Prophet Muhammed (Peace Be Upon Him ) made the utmost effort to clarify the reality of the Mercy of Allah (S.W.T.) with His servants so that Muslims will be merciful among one another and be merciful with others, and know that this mercy is the way to gain the mercy of Allah.

1) Narrated Abu Huraira (Radhi-Allah-hu ‘anhu): The Messenger of Allah (salAllahu alayhi wa sallam) said: “When Allah completed the creation, He wrote in His Book which is with Him on His Throne, “My Mercy overpowers My Anger.”[Sahih Bukhari – Book: 54. Beginning of Creation, Hadith:416]

99 parts of Mercy Allah kept with Him and sent down its only 1 part on the earth
2) Narrated Abu Huraira: I heard Allah’s Apostle says, Allah divided Mercy into one-hundred parts and He kept its ninety-nine parts with Him and sent down its one part on the earth, and because of that, its one single part, His creations are Merciful to each other, so that even the mare lifts up its hoofs away from its baby animal, lest it should trample on it.” [Bukhari Book 8 Volume 73 Hadith 29]

Disbelievers have absolutely no hope of Allah’s Mercy
1) “O my sons! Go you and enquire about Yusuf (Joseph) and his brother, and never give up hope of Allah’s Mercy. Certainly, no one despairs of Allah’s Mercy, except the people who disbelieve.” [Quran 12/87]