Answer:
The free Google service that sends notifications by mail is "Google Alerts"
Step-by-step explanation:
"Google Alerts" is a service that automatically notifies the user via email about new results on a Google Search topic.
There are currently 6 types of alerts that match depending on the results and search terms of the user:
1) News
2) Web
3) Videos
4) Blogs
5) Groups
6) All