Hadiths about Tahajjud (The Night Prayer):

Narrated Abu Huraira (Radiallahu anhu): Allah’s Apostle (Peace be upon him) said, “Our Lord, the Blessed, the Superior, comes every night down on the nearest Heaven to us when the last third of the night remains, saying: “Is there anyone to invoke Me, so that I may respond to invocation? Is there anyone to ask Me, so that I may grant him his request? Is there anyone seeking My forgiveness, so that I may forgive him?” [Bukhari]

Abd Allah ibn Salam (Allah be pleased with him) reports that the Messenger of Allah (blessings and peace be upon him, his family, and companions) said, “O people! Spread the salams, feed others, maintain family ties, and pray at night when others sleep and you will enter Heaven safely.” [Tirmidhi, Hakim]

Abu Umama al-Bahili (Allah be pleased with him) reports that the Messenger of Allah (blessings and peace be upon him, his family, and companions) said, “Hold tight to night prayer, for it was the way of the righteous before you, a way of drawing closer to your Lord, an expiation for wrong deeds, and a shield from sin.” [Tirmidhi] 

Allah has praised those who wake up at night for His remembrance, supplication, and to seek forgiveness and entreat Him, saying,‘They forsake their beds to cry unto their Lord in fear and hope, and spend of what We have bestowed on them. No soul knows what is kept hid from them of joy, as a reward for what they used to do.’ [Qur’an, 32: 16-17]

And He said, “those who pray and beg Allâh’s Pardon in the last hours of the night.” [Qur’an, 3: 17]

And, ‘[The (faithful) servants of the Merciful are they who walk upon the earth modestly, and when the foolish one address them answer: Peace;] And who spend the night before their Lord, prostrate and standing…’ [Qur’an, 25: 63-64]

Is one who is obedient to Allâh, prostrating himself or standing (in prayer) during the hours of the night, fearing the Hereafter and hoping for the Mercy of his Lord (like one who disbelieves)? Say: “Are those who know equal to those who know not?” It is only men of understanding who will remember (i.e. get a lesson from Allâh’s Signs and Verses).  [Qur’an, 39: 9]” 

It is disliked to leave the night prayer (Tahajjud) for one who has made it their habit, unless there is an excuse.

The Prophet Muhammad (Allah bless him and give him peace) said to Ibn Umar (Allah be pleased with him), “O Abd Allah! Do not be like so-and-so. He used to pray at night and then left it.” [Bukhari and Muslim]

The Messenger of Allah (blessings and peace be upon him, his family, and companions) said, “The most beloved of actions to Allah are the most constant, even if little.” [Bukhari and Muslim] [Ibn Abidin, Radd al-Muhtar, from Ibn Amir Haajj’s Halba]

It is recommended to start the night vigil with two short rakats, because of the hadith of Abu Hurayra that the Prophet Muhammad (Allah bless him and give him peace) said, “If you get up for night prayer, start with two short rakats.” [Muslim, Ahmad, Abu Dawud]