i'm an upcoming webmaster and I want to know if it is legal to put the link of another website in my site without asking them.

I personally don't see why not. In the end, you are driving traffic to their site for them and they aren't paying you a kobo

On the other hand, if they notice an increase in traffic from your site and for whatever reason, they would rather their URL not be that public, they might send you correspondence asking you to stop, failure of which may result in legal actions.

I hope this helps.