Significance of the First Ten Days of Zul Hijjah
Allah has taken oath of ten nights in Surah Al-Fajr. According to the majority of the commentators of Qur’an, the nights are those of the (first) ten days of Zul-Hijjah
Abdullah Ibn ‘Abbas Radiyallaahu anhu related that the Prophet Sallallaahu Alayhi Wasallam said, “Good deeds performed on other days are not superior to those performed on these (first ten days of Zul Hijjah).” The Companions Radiyallaahu anhum inquired, “Not even Jihad?” He replied, “Not even Jihad, except for that person who goes out putting himself and his wealth in danger and does not return with anything (Bukhãri)

Abdullah Ibn ‘Abbas Radiyallaahu anhu narrated that Rasulullah Sallallaahu Alayhi Wasallam said, “On no other days are good deeds more liked by Allah than on these ten days (i.e. The first ten days of Zul Hijjah).” The Sahabah Radiyallaahu anhum asked, “O Rasulullah ! Not even Jihad in the Way of Allah?” Rasulullah Sallallaahu Alayhi Wasallam replied, “Not even Jihad in the Way of Allah, except for that person who goes out with his life and wealth and does not return with anything.” (Aboo Dãwood, Tirmidhi)

Aboo Hurayrah Radiyallaahu anhu related that Rasulullah Sallallaahu Alayhi Wasallam said, “On no days is the worship of Allah desired more than in the (first) ten days of Zul Hijjah. The fast of each of these days is equal to the fast of a whole year, and the worship of each of these nights is equal to the worship of Laylatul Qadr.” (Tirmidhi)
The mother of the believers, Hafsah Radiyallaahu anhaa reports that Rasulullah Sallallaahu Alayhi Wasallam used to fast the (first) nine days of Zul Hijjah. (Nasã’ee,Ahmad)
Abdullah Ibne ‘Umar Radiyallaahu anhu related that Rasoolullah Sallallaahu Alayhi Wasallam said, “No days are as weighty with Allah and so liked by Him for good deeds than the first ten days of Zul Hijjah. So on these days increasingly read Subhãnallah, Lã ilãha illallãh, Alhamdulillah and Allahu Akbar.” (Musnad Ahmad)

Virtues of the Day of Arafah (9th Zul Hijjah)
‘Aaishah Radiyallaahu Anha reports that Rasulullah Sallallaahu Alayhi Wasallam said, “There is no day in which Allah sets free more souls from the fire of hell than on the day of Arafat. And on that day Allah draws near to the earth and by way of exhibiting His Pride remarks to the angels, ‘What is the desire of these (servants of mine)?” (Muslim)

Talhah Radiyallaahu anhu reports that Rasulullah Sallallaahu Alayhi Wasallam said, “Apart from the day of the Battle of Badr there is no day on which the Shay tan is seen to be more humiliated, more rejected, more depressed and more infuriated, than on the day of Arafat, and indeed all this is only because of beholding the abundance of descending mercy (on the day) and Allah’s forgiveness of the great sins of the servants.” (Mishkãt)

Aboo Qatãdah Al-Ansãri Radiyallaahu anhu narrated that Rasulullah Sallallaahu Alayhi Wasallam was asked about the fast on the day of Arafat. He said, “It compensates for the (minor) sins of the past and the coming year.” (Muslim, Tirmizi, Ibne Mãjah)

Night of ‘Eidul Adha
The nights of both ‘Eid are described in the Hadith as amongst the great and sacred nights in the Muslim calendar. To remain awake on the nights of ‘Eid and perform ‘ibãdah is a source of great virtue and reward.

Aboo Umarah radhiallahu anhu related that ‘Aaishah Radiyallaahu Anha reports that Rasulullah Sallallaahu Alayhi Wasallam said, “Whosoever stays awake and performs ‘Ibadah (worship) on the nights of the two ‘Eid, with hope for abundant reward (from Allah), his heart will not die on the day (i.e. Qiyãmah) when all hearts will be dead.” (Targheeb & Ibn Majah)

Virtues of Qurbani/Udhiya
Rasulullah Sallallaahu Alayhi Wasallam said, “There is nothing dearer to Allah during the days of Qurbani than the sacrificing of animals. The sacrificed animal shall come on the Day of Judgement with its horns, hair, and hooves (to be weighed). The sacrifice is accepted by Allah before the blood reaches the ground. Therefore sacrifice with an open and happy heart.” (Tirmidhi, Ibne Mãjah)

Takbirãt of Tashreeq
The Takbirãt of Tashreeq are:

Allahu Akbar, Allahu Akbar,Lã ilãha illallãhu wallahu Akbar,Allahu Akbar, Walil lahil hamd.

“Allah is the Greatest, Allah is the Greatest.There is no deity besides Allah and Allah is the Greatest. Allah is the Greatest and all praises are for Allah only.”

It is Wajib (according to the Hanafi school of thought) for every adult Muslim to recite these Takbiraat of Tashreeq audibly once after every Fardh salaah which is performed with Jamaat (congregation) from the Fajr of 9th Zul Hijjah to the ‘Asr of 13th Zul Hijjah (i.e. total of 23 Salaah).

Mas’alah: It is not wãjib for women and shar’ee travellers. But, if they are performing salãh behind an imãm upon whom it is wãjib, then it will become wãjib upon them too. However it is mustahab for them to recite in any case.

Mas’alah: Women should not say it loudly but softly.
Mas’alah: Takbeer should be recited immediately after concluding the fardh prayer.

Have yourself a Blessed 10 days and Eid Mubark!!