Allah Almighty says in the Holy Quran:
إِنَّ عِدَّةَ ٱلشُّهُورِ عِندَ ٱللَّهِ ٱثۡنَا عَشَرَ شَهۡرࣰا فِی كِتَـٰبِ ٱللَّهِ یَوۡمَ خَلَقَ ٱلسَّمَـٰوَ ٰتِ وَٱلۡأَرۡضَ مِنۡهَاۤ أَرۡبَعَةٌ حُرُمࣱۚ ذَ ٰلِكَ ٱلدِّینُ ٱلۡقَیِّمُۚ فَلَا تَظۡلِمُوا۟ فِیهِنَّ أَنفُسَكُمۡۚ
Indeed, the number of months ordained by Allah is twelve—in Allah’s Record since the day He created the heavens and the earth—of which four are sacred. That is the Right Way. So do not wrong one another during these months.
This series of months and years has been continued by Allah Almighty since the day Allah created this world. The system of the universe has been operating in the same order from the beginning.
Out of the twelve months of the Islamic year, four months have been declared sacred by Allah. During these sacred months, it is incumbent upon every Muslim not to wrong himself by committing sins and not to harm any of his Muslim brothers. Even no Muslim government is allowed to launch an attack on the infidels by violating the sanctity of these four months. However, jihad against the infidels is a great act. But it is a great thing not to take the initiative against them in these months.
The number of sacred months is contained in the Sahih Hadith. The Holy Prophet صلى الله عليه وسلم said:
إنَّ الزَّمانَ قَدِ اسْتَدارَ كَهَيْئَتِهِ يَومَ خَلَقَ اللَّهُ السَّمَواتِ والأرْضَ، السَّنَةُ اثْنا عَشَرَ شَهْرًا، مِنْها أرْبَعَةٌ حُرُمٌ، ثَلاثٌ مُتَوالِياتٌ: ذُو القَعْدَةِ، وذُو الحِجَّةِ، والمُحَرَّمُ، ورَجَبُ، مُضَرَ الذي بيْنَ جُمادى، وشَعْبانَ.
Time has come back to its original state which it had when Allah created the Heavens and the Earth; the year is twelve months, four of which are sacred. Three of them are in succession; Dhul-Qa’da, Dhul-Hijja and Al-Muharram, and (the fourth being) Rajab Mudar (named after the tribe of Mudar as they used to respect this month) which stands between Jumad (ath-thani) and Sha’ban.
(صحيح البخاري ٤٦٦٢)
The month of Dhul Hijjah is sacred as well as the month of Hajj. Hajj becomes obligatory on the able-bodied Muslims in this month.
The first thirteen days of Dhul Hijjah are of great importance to all Muslims. The Holy Prophet صلى الله عليه وسلم mentioned the superiority of the first decade of this month as:
مَا الْعَمَلُ فِي أَيَّامِ الْعَشْرِ أَفْضَلَ مِنَ الْعَمَلِ فِي هَذِهِ ”. قَالُوا وَلاَ الْجِهَادُ قَالَ ” وَلاَ الْجِهَادُ، إِلاَّ رَجُلٌ خَرَجَ يُخَاطِرُ بِنَفْسِهِ وَمَالِهِ فَلَمْ يَرْجِعْ بِشَىْءٍ
No good deeds done on other days are superior to those done on these (first ten days of Dhul Hijjah).” Then some companions of the Prophet (ﷺ) said, “Not even Jihad?” He replied, “Not even Jihad, except that of a man who does it by putting himself and his property in danger (for Allah’s sake) and does not return with any of those things.
(صحيح البخاري: 969)
If it becomes clear to us the priority of working in the ten days of Dhul-Hijjah over other days, and that this decade is a blessing and favor from Allah to His servants, and a great opportunity that must be seized, then it is necessary for us to focus on these ten days with more care and attention, and to be keen on. We should struggle with obedience in it, and to multiply the goodness and types of acts of obedience, as this was the case of the righteous predecessors in this decade.
The following actions are considered desirable during the month of Dhul Hijjah.
They are the best that can be done in the ten days of Dhul-Hijjah, and for whomever Allah makes it easy for him to perform the pilgrimage to his house or perform Umrah in the required manner, his reward is Paradise. For the Prophet, may صلى الله عليه وسلم, said: (Umrah to Umrah is an expiation for what is between them, and an accepted Hajj has no reward except Paradise) [متفق عليه]. The accepted Hajj is the Hajj that is consistent with the guidance of the Prophet, صلى الله عليه وسلم which was not mixed with sins such as hypocrisy, reputation, obscenity or immorality and is surrounded by good deeds.
It falls under the category of righteous deeds, rather it is one of the best of them, and Allah has added it to Himself due to the greatness of its stature. so He, Glory be to Him, said in the Qudsi hadith: (Every deed of the son of Adam is for him except fasting, for it is for Me and I reward it) [متفق عليه].
The Prophet,صلى الله عليه وسلم ,singled out fasting on the day of Arafah from among the ten days of Dhul-Hijjah with greater care, and explained the virtue of fasting by saying: (Fasting on the day of Arafah, I hope that Allah will expiate the sins for the year before and after it) [صحيح مسلم].
Accordingly, it is Sunnah for a Muslim to fast on the nine days of Dhul-Hijjah, because the Prophet, صلى الله عليه وسلم urged good deeds during it. Imam Al-Nawawi went to the recommendation of fasting for ten days and said: Fasting them is strongly recommended.
And it is for the sake of deeds, the greatest and the most virtuous, and that is why the Muslim must preserve them in their times with the congregation, and he must do a lot of supererogatory praying during these days, for they are among the best acts of worship, and the Prophet, صلى الله عليه وسلم, said in what he narrated from his Lord: A Muslim remains offering supererogatory prayers until I love him) [صحيح بخاري].
Takbeer, praise, tahlil and remembrance:
On the authority of Ibn Umar, رضي الله عنهما, on the authority of the Prophet, صلى الله عليه وسلم he said: “There are no days greater and more liked to Allah than these ten days, so multiply during them in terms of tahlil, takbeer and praise” [مسند أحمد].
Sayyiduna Abuhurairah and Ibn Umar رضي الله عنهما both go out to the market in the ten days uttering takbeer and tahmeed loudly and the people say takbeer by seeing them. And he said: Umar used to say the takbeer in his dome in Mina, so the people of the mosque would hear him say takbeer, and the people of the markets would recite the takbeer until Mina shook. Ibn Umar used to grow up in Mina those days, behind the prayers, on his bed, and in his tents, sittings and walks all those days.
It is desirable for a Muslim to recite the takbeer aloud during these days of Dhul Hijjah and to raise his voice with it, and he must beware of the collective takbeer, as it was not transmitted from the Prophet, صلى الله عليه وسلم nor from any of the predecessors, and the Sunnah is that each one should recite takbeer on his or her own.
And it is among the number of righteous deeds that a Muslim should give charity within these days of Dhul Hijjah, and Allah urged it, saying: (O you who believe, spend from what We have provided you before a day comes in which there is no bargaining, friendship, or intercession, and the unbelievers are the wrongdoers) [Al-Baqarah: 254].
Take a look at some books on the topics of Hajj, that may interest you.