Can a mother give up her parental rights?

Hi. I was just wondering can a mother give up her parental rights, not like in an adoption way but if the father wanted the child and she didn't, could she do that or can it be done unoffically without the law? Or if it has to be done by law, if she wanted to, could she reinstate her rights at a later date? How do you sign away your rights anyway? I'm not trolling, just curious and I couldn't find anything about it on google and what I did find was mostly related to dads. Thanks :)