Send newsletter with list of users with specific field value Is there a module to send a newsletter with a list of users with the same interests?
There is the simplenews module which will do the newsletter sending part of your question but similar interests is up to you to define. Drupal can't predict what "similar interests" are!

If you already have a list of users with similar interests, simplenews will enable you to create individual groups/mailing lists which you could add your users to.