Al-Mundhiri recorded the following chapter in his book Al-Targhib wal-Tarhib:

الترغيب في صيام رمضان احتسابا وقيام ليله سيما ليلة القدر وما جاء في فضله

Encouragement to perform fasting in the month of Ramadan seeking reward and standing for prayer at night, especially on the Night of Decree, and what was been related of its virtues.

Source: al-Targhīb wal-Tarhīb 2/90

Abu Huraira reported: The Messenger of Allah, peace and blessings be upon him, said:

مَنْ صَامَ رَمَضَانَ إِيمَانًا وَاحْتِسَابًا غُفِرَ لَهُ مَا تَقَدَّمَ مِنْ ذَنْبِهِ وَمَنْ قَامَ لَيْلَةَ الْقَدْرِ إِيمَانًا وَاحْتِسَابًا غُفِرَ لَهُ مَا تَقَدَّمَ مِنْ ذَنْبِهِ

Whoever fasts the month of Ramadan due to faith and seeking reward, his previous sins will be forgiven. Whoever stands in prayer on the Night of Decree due to faith and seeking reward, his previous sins will be forgiven.

Source: Ṣaḥīḥ al-Bukhārī 1901, Grade: Muttafaqun Alayhi

Abu Huraira reported: The Messenger of Allah, peace and blessings be upon him, encouraged standing for night prayer in the month of Ramadan, without imposing it on them. The Prophet would say:

مَنْ قَامَ رَمَضَانَ إِيمَانًا وَاحْتِسَابًا غُفِرَ لَهُ مَا تَقَدَّمَ مِنْ ذَنْبِهِ

Whoever stands in prayer during Ramadan due to faith and seeking reward, his previous sins will be forgiven.

Source: Ṣaḥīḥ al-Bukhārī 2009, Grade: Muttafaqun Alayhi

Abu Sa’id al-Khudri reported: The Messenger of Allah, peace and blessings be upon him, said:

مَنْ صَامَ رَمَضَانَ وَعَرَفَ حُدُودَهُ وَتَحَفَّظَ مِمَّا كَانَ يَنْبَغِي لَهُ أَنْ يَتَحَفَّظَ فِيهِ كَفَّرَ مَا قَبْلَهُ

Whoever fasts the month of Ramadan, acknowledging its limits and guarding what should be guarded in it, then it will expiate sins which came before it.

Source: Musnad Aḥmad 11310, Grade: Hasan

Abu Huraira reported: The Messenger of Allah, peace and blessings be upon him, said:

الصَّلَوَاتُ الْخَمْسُ وَالْجُمُعَةُ إِلَى الْجُمُعَةِ وَرَمَضَانُ إِلَى رَمَضَانَ مُكَفِّرَاتٌ مَا بَيْنَهُنَّ مَا اجْتُنِبَتْ الْكَبَائِرُ

The five prayers, Friday to Friday, and Ramadan to Ramadan will expiate the sins committed between them, as long as major sins are avoided.

Source: Ṣaḥīḥ Muslim 233, Grade: Sahih

Abu Huraira reported: The Prophet, peace and blessings be upon him, ascended the pulpit and he said:

آمِينَ آمِينَ آمِينَ

Amin, amin, amin.

It was said, “O Messenger of Allah, you ascended the pulpit and said amin, amin, amin.” The Prophet (ṣ) said:

إِنَّ جِبْرِيلَ أَتَانِي فَقَالَ مَنْ أَدْرَكَ شَهْرَ رَمَضَانَ وَلَمْ يُغْفَرْ لَهُ فَدَخَلَ النَّارَ فَأَبْعَدَهُ اللَّهُ قُلْ آمِينَ فَقُلْتُ آمِينَ وَمَنْ أَدْرَكَ أَبَوَيْهِ أَوْ أَحَدَهُمَا فَلَمْ يَبَرَّهُمَا فَمَاتَ فَدَخَلَ النَّارَ فَأَبْعَدَهُ اللَّهُ قُلْ آمِينَ فَقُلْتُ آمِينَ وَمَنْ ذُكِرْتُ عِنْدَهُ فَلَمْ يُصَلِّ عَلَيْكَ فَمَاتَ فَدَخَلَ النَّارَ فَأَبْعَدَهُ اللَّهُ قُلْ آمِينَ فَقُلْتُ آمِينَ

Verily, Gabriel came to me and he said: Whoever reaches the month of Ramadan and he is not forgiven, then he will enter Hellfire and Allah will cast him far away, so say amin. I said amin. Whoever sees his parents in their old age, one or both of them, and he does not honor them and he dies, then he will enter Hellfire and Allah will cast him far away, so say amin. I said amin. Whoever has your name mentioned in his presence and he does not send blessings upon you and he dies, then he will enter Hellfire and Allah will cast him far away, so say amin. I said amin.

Source: Ṣaḥīḥ Ibn Ḥibbān 915, Grade: Sahih

Abu Huraira reported: The Messenger of Allah, peace and blessings be upon him, said:

إِذَا دَخَلَ شَهْرُ رَمَضَانَ فُتِّحَتْ أَبْوَابُ السَّمَاءِ وَغُلِّقَتْ أَبْوَابُ جَهَنَّمَ وَسُلْسِلَتِ الشَّيَاطِين‏

When the month of Ramadan begins, the gates of the heaven are opened and the gates of Hellfire are closed and the devils are chained.

Source: Ṣaḥīḥ al-Bukhārī 1899, Grade: Muttafaqun Alayhi

In another narration, the Prophet said:

إِذَا كَانَ أَوَّلُ لَيْلَةٍ مِنْ شَهْرِ رَمَضَانَ صُفِّدَتْ الشَّيَاطِينُ وَمَرَدَةُ الْجِنِّ وَغُلِّقَتْ أَبْوَابُ النَّارِ فَلَمْ يُفْتَحْ مِنْهَا بَابٌ وَفُتِّحَتْ أَبْوَابُ الْجَنَّةِ فَلَمْ يُغْلَقْ مِنْهَا بَابٌ وَيُنَادِي مُنَادٍ يَا بَاغِيَ الْخَيْرِ أَقْبِلْ وَيَا بَاغِيَ الشَّرِّ أَقْصِرْ وَلِلَّهِ عُتَقَاءُ مِنْ النَّارِ وَذَلكَ كُلُّ لَيْلَةٍ

On the first night of the month of Ramadan, the devils are chained, the jinn are restrained, and the gates of Hellfire are closed and none of its gates are opened. The gates of Paradise are opened and none of its gates are closed. A caller announces: O seeker of good, come near! O seeker of evil, stop short! Allah will save them from the Hellfire and that is during every night of Ramadan.

Source: Sunan al-Tirmidhī 682, Grade: Sahih

And in another narration, the Prophet said:

قَدْ جَاءَكُمْ رَمَضَانُ شَهْرٌ مُبَارَكٌ افْتَرَضَ اللَّهُ عَلَيْكُمْ صِيَامَهُ تُفْتَحُ فِيهِ أَبْوَابُ الْجَنَّةِ وَيُغْلَقُ فِيهِ أَبْوَابُ الْجَحِيمِ وَتُغَلُّ فِيهِ الشَّيَاطِينُ فِيهِ لَيْلَةٌ خَيْرٌ مِنْ أَلْفِ شَهْرٍ مَنْ حُرِمَ خَيْرَهَا قَدْ حُرِمَ

The month of Ramadan has come, a blessed month in which Allah Almighty has obligated you to fast. In it the gates of the heavens are opened, and in it the gates of Hellfire are closed, and in it the devils are chained, and in it is a night that is better than a thousand months. Thus, whoever is deprived of its good is truly deprived.

Source: Musnad Aḥmad 7148, Grade: Sahih

Anas ibn Malik reported: The Messenger of Allah, peace and blessings be upon him, said when the month of Ramadan began:

إِنَّ هَذَا الشَّهْرَ قَدْ حَضَرَكُمْ وَفِيهِ لَيْلَةٌ خَيْرٌ مِنْ أَلْفِ شَهْرٍ مَنْ حُرِمَهَا فَقَدْ حُرِمَ الْخَيْرَ كُلَّهُ وَلَا يُحْرَمُ خَيْرَهَا إِلَّا مَحْرُومٌ

Verily, this month has presented itself to you. There is a night within it that is better than a thousand months. Whoever is deprived of it has been deprived of all good. None is deprived of its good but that he is truly deprived.

Source: Sunan Ibn Mājah 1644, Grade: Sahih

Jabir reported: The Messenger of Allah, peace and blessings be upon him, said:

إِنَّ لِلَّهِ عِنْدَ كُلِّ فِطْرٍ عُتَقَاءَ وَذَلِكَ فِي كُلِّ لَيْلَةٍ

Verily, Allah has people He redeems at the time of breaking fast, and that is during every night.

Source: Sunan Ibn Mājah 1643, Grade: Sahih

Abu Sa’id al-Khudri reported: The Messenger of Allah, peace and blessings be upon him, said:

إِنَّ لِلَّهِ عُتَقَاءَ فِي كُلِّ يَوْمٍ وَلَيْلَةٍ يعني في رمضان لِكُلِّ عَبْدٍ مِنْهُمْ دَعْوَةٌ مُسْتَجَابَةٌ

Verily, Allah has people He redeems in every day and night of Ramadan. Every servant among them has a supplication that will be answered.

Source: Musnad Aḥmad 7450, Grade: Sahih

‘Amr ibn Murrah reported: A man came to the Prophet, peace and blessings be upon him, and he said, “O Messenger of Allah, what do you think if I testify there is no God but Allah and you are the Messenger of Allah, I perform the five prayers, I pay the obligatory alms, I fast the month of Ramadan and stand for prayer in it. Among whom will I be?” The Prophet said:

مِنَ الصِّدِّيقِينَ وَالشُّهَدَاءِ

Among the truthful and the martyrs.

Source: Ṣaḥīḥ Ibn Ḥibbān 3492, Grade: Sahih

Abu Ayyub reported: The Messenger of Allah, peace and blessings be upon him, said:

مَنْ صَامَ رَمَضَانَ ثُمَّ أَتْبَعَهُ سِتًّا مِنْ شَوَّالٍ كَانَ كَصِيَامِ الدَّهْرِ

Whoever fasts the month of Ramadan and then follows it with six days of fasting in the month of Shawwal, it will be as if he fasted for the entire year.

Source: Ṣaḥīḥ Muslim 1164, Grade: Sahih

Thawban reported: The Messenger of Allah, peace and blessings be upon him, said:

صِيَامُ رَمَضَانَ بِعَشَرَةِ أَشْهُرٍ وَصِيَامُ السِّتَّةِ أَيَّامٍ بِشَهْرَيْنِ فَذَلِكَ صِيَامُ السَّنَةِ

Fasting the month of Ramadan is like ten months of fasting and fasting six days of Shawwal is like two months of fasting. Thus, they are like fasting for a year.

Source: Ṣaḥīḥ Ibn Khuzaymah 2115, Grade: Sahih