DHUL HIJJAH or ZILHIJJAH
Dhul Hijjah or Zilhijjah is the twelfth and last month of the Islamic Calendar based on lunar system. This is a very sacred month in the Muslim calendar, marking the end of the year. It is in this month in which the Hajj (pilgrimage) takes place.
"Dhu al-Hijjah" literally means "Possessor of the Pilgrimage." During this month pilgrims from all around the world congregate at Makkah, Saudi Arabia to perform Hajj. The actual pilgrimage rites take place on the 8th to 13th days of this month. Day of Arafah takes place on the ninth of this month. Eid al-Adha, the "Festival of the Sacrifice", begins on the tenth day and ends on the thirteenth of Dhul-Hijjah. 
Dhul Hijjah is a great and sacred month in which the Hajj (annual Pilgrimage to Makkah) takes place. It is a month in which blessings are plentiful and Allah takes care of people’s needs. In it are the “ten nights” which Allah swears by in the Qur’an.Surah Fajr 89:1-3. The majority of Tafseer scholars have stated that Allah is referring here to the ten nights of Dhul Hijjah, Tafseer Ibn Kathir, Qur’an. Surah Fajr 89: 2.
The month of Dhul-Hijjah is a season of worship, and seasons of worship bring along blessings, benefits and opportunities to correct one's faith and make up for shortcoming. Every one of these special opportunities involves some kind of worship, which brings the slave closer to his Lord. And Allah bestows His blessings and Favors on whom He wills. The fortunate person is he who makes good use of these special months, days, and hours, while worshiping Allah. He is most likely to be touched by the blessings of Allah. [Ibn Rajab, al-Lataa'if pp. 8]
According to the Prophet Muhammad (May Allah honour Him and grant Him peace) the first ten days of this month are a special time for devotion. Even for those who are not traveling for the pilgrimage, this is a special time to remember Allah and spend extra time in devotion and good deeds. The first ten days of Dhul-Hijjah are called as layali ashra in the Qur’an. Surah Fajr 89: 2 and 11,12 and 13th of Dhul Hijjah are called as Ayyam e Tashreeq.
The month of Dhul-Hijjah is indeed a month of tremendous virtues and blessings. The First Ten Days of this month are especially significant and are among the most magnificent days in the Islamic calendar. It is reported from Ibn Abbas (R) that Prophet Muhammad (May Allah honour Him and grant Him peace) said: " There is no day wherein any good action is more beloved to Allah than these ten days (the first ten days of Dhul Hijjah)". The Sahabah (Companions of Prophet Muhammad (May Allah honour Him and grant Him peace)) enquired: "Not even Jihad in the path of Allah ? "(i.e., are actions performed in these days more beloved than even the act of Jihad)", with the exception of that person who left with his life and wealth (in the path of Allah) and did not return with any of it (i.e. he is martyred)". Sahih Al Bukhari, Vol 2:457
No days are as weighty with Allah and so liked by Him for good deeds than the first ten days of Dhul-Hijjah ". Therefore in these days increasingly recite: "La ilaha illallah, Allahu Akbar, Al-Hamdu-lillah, Sub-hanallah."
These texts and others indicate that these ten days are better than all the other days of the year, with no exceptions, not even the last ten days of Ramadaan. But the last ten nights of Ramadaan are better, because they include Laylat al-Qadr ("the Night of Power"), which is better than a thousand months. Thus the various reports may be reconciled. (Tafseer Ibn Kathir, Vol 5/412)
The Prophet (May Allah honour Him and grant Him peace)encouraged people to do righteous deeds because of the virtue of this season for people throughout the world, and also because of the virtue of the place - for the Hujjaaj (pilgrims) to the Sacred House of Allah.
‘Abdullaah ibn ‘Umar (R) reported that the Prophet (May Allah honour Him and grant Him peace)said: "There are no days greater in the sight of Allah and in which righteous deeds are more beloved to Him than these ten days, so during this time recite a great deal of Tasbeeh ("Subhan-Allah"), Tahleel ("La ilaaha ill-Allah"), Takbeer ("Allahu akbar") and Tahmeed ("Al-hamdu Lillaah")."Book of Musnad Ahmad, Vol 7:224
Abu Qatadah (R) is reported to have said that the Prophet (May Allah honour Him and grant Him peace) said: "Fasting on the day of `Arafah is an expiation (of sins) for two years, the year preceding it and the year following it, Sunan Nisa’i, Vol 4:205 and by Abu Dawud; classified by al-Albaani as saheeh in Saheeh Abi Dawud, Vol 2:462.
Concerning the types of worship to be performed during these ten days: one must understand that these days are a great blessing from Allah to His slave, which is appreciated properly by the actively righteous deeds. Therefore the good deeds which the Muslim should strive to do during the first ten days of Dhu’l-Hijjah are: