Who gave two nation theory?

Sir Syed Ahmed Khan was regarded as the principal architect of the Two-Nation theory as he provided a modern idiom in which to express the quest for Islamic identity.

The two-nation theory is an ideology of religious nationalism which significantly influenced the Indian subcontinent following its independence from the British Empire.

For further reading check the following articles:

• List of Socio-Religious Movements
• Lucknow Pact
• Indian Education System During British Rule