Mailman (usually provided for free with a cPanel backend control panel on Unix hosting) does a good job with mailing lists. This is one-to-all email, not necessarily a newsletter that everyone in the group can use. Pretty simple software, but it works well. Here’s a quick video showing how to add a new member to a list or remover an existing member from a list. Click image to left to view video.
Related posts:
Thank you, it’s a good resources