I want to know that what are the main holy nights during which we are asked by allah to wake all night and offer Prayers ,

Assalaam alaikum,

Here are some information regarding the night prayer,which is recommended practice to do naafil salat later part of the night.

Islam Question and Answer - The virtues of Qiyaam (prayer at night) during Ramadaan
Islam Question and Answer - Is Witr prayer different from the night prayer?
Islam Question and Answer - Sunnah (Prophet's Example) in Performing Night Prayer

Wa alaikum salaam