Miraculous Splitting/Division of the Moon by Muhammad (sws)

The people of Makkah asked Prophet Muhammad (sws) for a sign of his prophethood, so the moon was miraculously divided into two, until they could see Al-Harra (a place) between the two halves. It was a full mooon night when the moon was split.
This is also mentioned in the Quran, in Surah Al-Qamar:

Ibn Kathir referenced the hadiths about the splitting of the moon in his Tafsir of Surah Al-Qamar, citing numerous authentic (sahih) hadiths on the matter.

1. The Authentic Reports

Hadith Authentic 1 - Sahih al-Bukhari: https://sunnah.com/bukhari:3638
Narrated Ibn `Abbas:
The moon was split into two parts during the lifetime of the Prophet.

Hadith Authentic 2 - Sahih al-Bukhari: https://sunnah.com/bukhari:3868
Narrated Anas bin Malik:
The people of Mecca asked Allah's Messenger (ﷺ) to show them a miracle. So he showed them the moon split in two halves between which they saw the Hira' mountain.

Hadith Authentic 3 - Tirmidhi: https://sunnah.com/tirmidhi:2182
Ibn 'Umar said:
"The moon split during the time of the Messenger of Allah(s.a.w), so the Messenger of Allah(s.a.w) said: 'Bear witness."'

Hadith Authentic 4 - Tirmidhi: https://sunnah.com/tirmidhi:3289
Narrated Muhammad bin Jubair bin Mut'im:
from his father who said: "The moon was split during the time of the Messenger of Allah (ﷺ) until it became as two sections, one above this mountain and one above that mountain. So they said: 'Muhammad has cast a spell upon us.' Some of them said: 'If he could cast a spell upon us, he can not cast a spell upon all of the people.'"

Authentic Hadith 5 - Sahih al-Bukhari: https://sunnah.com/bukhari:3869
Narrated `Abdullah:
The moon was split ( into two pieces ) while we were with the Prophet (ﷺ) in Mina. He said, "Be witnesses." Then a Piece of the moon went towards the mountain.

Hadith - Sahih al-Bukhari: https://sunnah.com/bukhari:3636
Narrated Abdullah bin Masud:
During the lifetime of the Prophet (ﷺ) the moon was split into two parts and on that the Prophet (ﷺ) said, "Bear witness (to thus).

2. Witnessed by many others throughtout Arabian Peninsula

This miracle was Witnessed by many people throughtout Arabian Peninsula. The disbelievers in Makkah, out of their arrogance, said "Muhammad has bewitched us.". So they said, "Wait and listen to what the travellers say, because Muhammad can't bewitch everyone". So the next day they asked the people who came to Makkah from outside, they all said that they also saw the Moon divided into two parts.

3. Witnessed by people in India too

Ibn Katheer said, "The moon-splitting was seen in many parts of the worold. It is said that it recorded in some parts of India. A building was built that night when the moon was split".

It is reported that during that time, there was king named Cheraman Perumal Rama Varma Kulashekhara in Kerala of India. He saw the miracle while he was relaxing on the rooftop of his palace in Kodungallore in a moonlit night. The king had come to know about Islam through Arab merchants and became more curious to know about the Prophet and his religion after the moon-splitting incident. Later, he converted to Islam. Read more here!