In The Name of Allah
The first ten days of dhul hijjah is better than all ther days Allah give us chance and opportunity to repent ,correct our faults and to do our best to draw nearer to Allah .So these days have espicial vitues , let us know these virtues:

Allah swears an oath by these days,and swearing an oath it shows its importance Allah says"By the dawn,By the ten nights" (al-fajr. this refers to the first ten days of Dhul Hijja.

the prophet (peace and blessing
be upon s him testified that these are the best days of this world ,Ibn Abbas (may Allah be pleased with him and his father ) reported that the prophet peace and blessing be upon said :"There are no days in which righteous deeds are more beloved to Allah than these days.the people asked "Not even Jihad for sake of Allah?" He said "Not even Jihad for sake of allah .except in the case of a man who went out to fight giving himself and his wealth up for the cause , and came back with nothing"

The prophet (beace and blessing be upon him )encourage people to do righteous deeds because the virtues of this days .
These days include the days of sacrifice and hajj .These days includ the day of arafaah,on which Allah perfected his religion . fasting on this day will expiate for the sins of two years

What should muslim do in these days:

1-fasting:it is the sunnah to fast on the ninth day of dhul hijjah ,because prophet urged us to do good deeds during this time , and fasting is one of the best of god deeds

2-Takbeer:it is sunnah to say takbeer 'Allahu akbar",tahmeed"al-hamdu-lillah" thahleel "la-illaha illa Allah" and tasbeeh'subhan allah" during the first ten days of dhul hijjah

Scrifice:Abu hurairah reported that the prophet (beace and blessing be upon him) said"the one who is able to offer a sacrifice ,but he does not should not attend our mosque

KHatma( completing of one reading of the whole Quran):
the prophet ( beace and blessing be upon him) said "whoever reads one letter of Allah's book shall have a hasana ,and each hasana has its tenflod.I do not say that Alif,Lam, Mim is one letter ,but Alif is letter,lam is a letter and mim is a letter.If you recite three parts of the Quran daily ,it is half a million hasana as adialy net profit

Repetance:the most important thing to repent to Allah and give up all kinds of sin

performing hajj and Umrah: one of the best deeds that one can do durring these days is to perform Hajj to the scared house of Allah