Correct: I'm looking forward to meeting you. The verb is--> 'to look forward to' = 'to anticipate' (transitive = requires a direct object). So, the direct object should be the (noun) form of the verb 'to meet', i.e. meeting. You could also use it like this : I'm looking forward to meeting you I'm looking forward for this job I'm looking forward to know you more I'm looking forward to get hired in your company I'm looking forward to hear from you you can also say it like this: I look forward to knowing you I look forward to meeting you here I look forward to trying your dish

"Look forward to." basically means something may happen or/is happening in the future that you think is good and want it to happen. It's a way of expressing "I can't wait."

Hola, "I look forward to hearing from you" is a common, formal way to end a letter. Tengo ganas de recibir noticias tuyas. Saludos, Simón.

expect (you can also use expectation)

Simply: anticipate with pleasure