Generally you have to work your notice period, in which time you can hand over your duties and responsibilities to someone else. However, sometimes there will be reasons When you want to make the notice period shorter. If you want to resign early, You have to include a waiver of your notice period in your resignation letter. For example, if your contract demands a month's notice, but your new employer wants you to join straight away, you can include a paragraph stating:
I am aware that my contract demands a notice period of (x) months, but I am required to join my new employer as early as possible. If you could therefore waive my notice period, I would be happy to help hand over responsibilities to my replacement.