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 (http://www.islam-qa.com/en/ref/3452/night%20prayer)
Islam Question and Answer - Is Witr prayer different from the night prayer? (http://www.islam-qa.com/en/ref/52875/night%20prayer)
Islam Question and Answer - Sunnah (Prophet's Example) in Performing Night Prayer (http://www.islam-qa.com/en/ref/282/night%20prayer%20ramadan)

Wa alaikum salaam