Although the four sacred months are not named in the Holy Qur-an, but their names are available from Ahadith (Sayings of Muhammad صلى الله عليه وسلم ).

The Messenger of Allah, Muhammad صلى الله عليه وسلم said in his farewell Khutbah (Sermon): “Time has completed its cycle and is as it was on the Day when Allah created the heavens and the earth. The year is twelve months, of which four are sacred, three consecutive months Dhul Qa’dah, Dhul Hijjah and Muharram – and the Rajab of Mudar which comes between Jumad al Ukhra and Sha’ban.”
Bukhari, Muslim

Allah (God) has also Commanded about maintaining the sanctity of the sacred months:

...يَا أَيُّهَا الَّذِينَ آمَنُوا لَا تُحِلُّوا شَعَائِرَ اللَّهِ وَلَا الشَّهْرَ الْحَرَامَ
You who believe! Violate not the sanctity of the Symbols of Allah, nor of the Sacred Months,...
Surah (Chapter) al-Ma"idah (The Table Spread with Food) 5:2

Muslims should live by a code of conduct ordained by Allah (God) that was demonstrated by His last Rasul (Messenger) all the time. They should pay special attention to respect the four months, because Allah (God) has given them a special status.

After migrating to Madinah, the Messenger of Allah, Muhammad صلى الله عليه وسلم saw the local Jews observe fasting on ‘Ashurah (Tenth day of Muharram). Upon enquiry, he found out that the Jews fast to commemorate the day when Allah (God) freed Musa عليه السلام (Moses) and his followers from the clutches of their tormentors - the people of Fir’aun (Pharaoh). The Messenger of Allah, Muhammad صلى الله عليه وسلم then began fasting on ‘‘Ashurah (Tenth day of Muharram) and commanded Muslims to do the same.

Ibn ‘Abbas رضي الله عنه narrated: “The Prophet صلى الله عليه وسلم came to Madinah and saw the Jews fasting on the day of ‘Ashurah. He asked, ‘What is this?’ They said, ‘This is a righteous day, it is the day when Allah saved the Children of Israel from their enemies, so Musa fasted on this day.’ He said, ‘We have more right to Musa than you,’ so he fasted on that day and commanded [the Muslims] to fast on that day.”
Bukhari

There are several more reports on this topic. Muslim reported it as follows:

“This is a righteous day” [the Jews said:] “This is a great day, on which Allah saved Musa and his people, and drowned Fir’aun (Pharaoh) and his people.”
“Musa fasted on this day… in thanksgiving to Allah, so we fast on this day.”

Another report from Ahmad adds:
“This is the day on which the Ark settled on Mount Judi, so Nuh fasted this day in thanksgiving.”

According to a tradition of ‘A”ishah bint Abu Bakr رضى الله عنها , the Quraysh of Makkah also fasted on the day of ‘Ashurah (Tenth day of Muharram).

The Jews of Madinah celebrated the day of ‘Ashurah (Tenth day of Muharram) with great fanfare.
The day of ‘Ashurah (Tenth day of Muharram) was venerated by the Jews, who took it as a festival. Muslim

The people of Khaybar (the Jews) used to take it as a festival and their women would wear their jewellery and symbols on that day. Muslim

The Messenger of Allah, Muhammad صلى الله عليه وسلم asked Muslims to be different from the Jews and observe fast.

‘So you (Muslims) should fast on that day.’ Bukhari

Ibn ‘Abbas رضي الله عنه narrated: “I never saw the Messenger of Allah صلى الله عليه وسلم so keen to fast any day and give it priority over any other than this day, the day of ‘Ashurah, and this month, meaning Ramadan.” Bukhari

Before his demise in the 11th Hijrah, the Messenger of Allah, Muhammad صلى الله عليه وسلم expressed his desire to fast for two consecutive days of Muharram, either on the 9th and 10th day of Muharram.

‘Abdullah bin ‘Abbas رضي الله عنه narrated: “When the Messenger of Allah صلى الله عليه وسلم fasted on ‘Ashurah and commanded the Muslims to fast as well, they said, ‘O Messenger of Allah, it is a day that is venerated by the Jews and Christians.’ The Messenger of Allah صلى الله عليه وسلم said, ‘If I live to see the next year, InshaAllah, we will fast on the ninth day too.’ But it so happened that the Messenger of Allah صلى الله عليه وسلم passed away before the next year came.” Muslim

It is Mustahab (Desirable) to observe fast on both the ninth and tenth days of the month of Muharram, because the Messenger of Allah, Muhammad صلى الله عليه وسلم fasted on the tenth day, and made intention to fast on the ninth.

It is highly desirable to make up for the missed Fard (Compulsory) fasts from the month of Ramadan before observing Nafl (Extra Obligatory) fast like the one on the ninth and tenth day of Muharram.

Coincidentally, on the tenth day of Muharram in the year 61H (Hijrah), fifty years after the demise by the Messenger of Allah, Muhammad صلى الله عليه وسلم , his grandson Husayn bin ‘Ali رضي الله عنه achieved Shahadah (Martyrdom) with his entire family in a heinous crime against humanity. This horrible crime was committed by the army of Yazid bin Mu’awiyah to save his un-Islamic dynastic rule and to silence the voice of Truth that rose against it.

A group of ignorant Muslims began associating the day of ‘Ashurah (Tenth day of Muharram) to this tragedy and instituted another set of Bid’at (Innovations) with the day.

They go for exaggerated grieving and mourning, spend the day without water, eulogizing and wailing, reciting poems of grief in a very sentimental manner, and tearing off their garments. They also slap themselves of their cheeks, beat their chests, hit themselves with chains and sharp objects, put dust in their hair and do excessive grieving and wailing.

The Messenger of Allah, Muhammad صلى الله عليه وسلم strictly forbade such display of sorrow and grief, as these were traditions from the days of pre-Islamic Jahiliyah (Ignorance).

Narrated Zaynab bint Umm Salama  رضى الله عنها : When Umm Habibah bint Abu Sufyan رضى الله عنها was informed of her father's death, she asked for perfume and rubbed it over her arms and said, "I am not in need of perfume, but I have heard the Prophet صلى الله عليه وسلم saying, "It is not lawful for a lady who believes in Allah and the Last Day, to mourn for more than three days except for her husband for whom the (mourning) period is four months and ten days."  
Bukhari, Book 63, Hadith 257

Many Bid’at (Innovations) have been associated with the day of ‘Ashurah (Tenth day of Muharram) by another group of ignorant Muslims who celebrate the day like ‘Id (Festival). Some of the Bid’at (Innovations) are taking out processions with replicas of the tomb of Husayn bin ‘Ali رضي الله عنه , applying Kohl and Henna, shaking hands with each other and cooking grains (Hubub) or other special dishes.

There is absolutely no evidence to this effect in any Sahih Hadith (Authentic Tradition of Muhammad صلى الله عليه وسلم ) or Da’if (Weak) tradition, nor is any evidence of this being done by any of his Sahabah (Companions). None of the Khulafa” (Caliphs) of the Muslims or anyone from the Tabi’in (Followers of Sahabah) encouraged or recommended such things.

From our sister website www.islam4theworld.net