Salah During Travel (Qasr)

Praying 5 times a day is an obligation upon Muslims. However, Allah has allowed His servants to shorten their Salah during travel.

1- Why Should We Follow Qasr Salah During Travel?
The Messenger of Allah (S.A.W.) said, 
“Verily, Allah loves for you to take His concessions, just as he dislikes you to be disobedient.” (Musnad Ahmad: 5832)
The shortening of prayers is mentioned in the Quran and is a confirmed Sunnah of Prophet Muhammad (S.A.W.): 
“And when you travel throughout the land, there is no blame upon you for the shortening Prayer” (Quran 4:101, An-Nasai: 457)
Hence, for travelers, it is permissible to shorten those Prayers that consist of 4 Rakat to only 2 Rakat (i.e. only Fardh Prayer of Dhuhr, Asr & Isha Salah).

2- Opinion of Different Fiqh:
According to Imam Shafii (R.A.) and Imam Ahmad bin Hanbal (R.A.), Reduction in the Prayer is not obligatory but merely optional. However, it is better to shorten it. 
Imam Abu Hanifah (R.A.) considers ‘Reduction in Prayer'’ as obligatory (Wajib) during travel .

3- Conditions for Qasr:
Travelling Distance
According to Imam Abu Hanifa, the minimum required distance for a person to be considered a traveler is when he or she intends to travel for 48 miles (80 kilometers approx) from his/her Waṭan-e-Aṣli (Original Hometown). 

Imam Shafi'i, Imam Ahmad bin Hanbal and Imam Malik fixed this distance at 55 miles approx (88 km approx).

Shortening of the prayers commences once a person leaves the city limits and ceases when they re-enter the city limits.
 
Period/Time
There is considerable scholarly disagreement on this matter from three days to four and to fifteen days.
Traveler-status is the intention to stay at the place of arrival for a period of:
Less than Fifteen (15) days [Hanafi]
Less than Four (4) days [Hanbali, Maliki and Shafii] - (Days of arrival and departure are not included)
 
4- How to do Taqseer (shortening of Prayers):
During travel, only Salah with 4 Rakat Fardh is to be shortened, i.e. Dhuhr, Asr & Isha. Travelers should offer 2 Rakat instead of 4 Rakat of the mentioned Salahs. 

However, 2 Rakat Fardh of Fajr and 3 Rakat of Maghrib Salah must be offered in full as you cannot cut 2 or 3 Rakat Fardh Salah in half.
When on a journey, the Prophet (S.A.W.) used to offer, without fail, 2 Sunnah Rakat of Fajr Prayer and 3 Rakat Witr with Isha Prayer. So these two should be offered even during traveling. 

Remember that these rules are only for a person who is traveling and offering individual Salah. If the traveler is praying in congregation then he must follow the Imam and offer the full Salah.