The Tarawih Prayer is Sunnat Mu'kkadah (compulsory)

Question :

Is the Tarawih prayer only Sunnah (i.c., supererogatory) or is it Sunnat Mu'kkadah (compulsory), and how do we perform it?

Answer:

It is Sunnat Mu'kkadah (compulsory) that the Prophet encouraged with his saying:
"Whoever stands for prayer (at night) during Ramadhan with faith and seeking reward, he will be forgiven for his previous sins."

It is confirmed that he prayed it with his Companions for a number of nights. Then he feared that it would be made obligatory upon them and he encouraged them to pray it by themselves. Thus, a man would pray it alone, and two men would pray it together and three would pray it in a group. Then 'Umar decided to gather them behind one man due to what that contained of bringing the people together for prayer and hearing the Qur'an. Thus, the Muslims continued upon this practice until today. During that time it was prayed as 23 Rak'ahs and they would lengthen the recitation (of the Qur'an) such that they would recite Surat Al-Baqarah in 12 Rak'ahs, and sometimes in 8 Rak'ahs. Since the Prophet did not set any restriction of a specific number on it, the matter concerning it (the number of Rak'ahs) is easy. If the person wishes he may lessen the number of Rak'ahs and lengthen the pillars (i.e., positions of the prayer), and if he wishes he may increase the number of Rak'ahs.

Source:
Ash-Shaykh Ibn Jibreen
Fatawa Islamiyah, Vol. 3 Pages 314-315