This objective can't be implemented in Process Builder alone, but it can be implemented in Process Builder with an autolaunched Flow. An Apex trigger, of course, could also achieve this.
If you pursued the Process Builder solution, your Process Builder would probably fire an autolaunched Flow that would use a lookup element to source all of the Contacts meeting your specific criteria. Then, a loop element over the Contacts could be used to accumulate the information you want to place in an email alert in a Flow variable. Finally, you can use a Send Email element to construct and send yourself the email alert.
You could extend and modify the same Flow to send email to users, or set off a workflow email alert to do so.
This would be a moderately complex PB + Flow setup. If you have not used those tools together before, you may way to try this Trailhead module, as well as the other modules covering Flow.