"I will not come to Delhi."

Translation: मैं दिल्ली नहीं आऊँगा ।

[CathyIsAwesome]

When do I use the different versions of "will come"? I am especially confused between when to use the one with, and the one without, the ऊँ

[DevendraPaliwal]

When you're talking about yourself "आऊंगा" is used. When you're talking about someone else, then "आएगा" is used.
e.g.
He will not come to Delhi.
वह दिल्ली नहीं आएगा।