Exchange is the server side of a collaborative application product that is part of the Microsoft Server infrastructure. Exchange's major features include email, calendaring, contacts and tasks, support for mobile and web-based access to information, and support for data storage.
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If you have the ability to run your entire Mail infrastructure - incoming + reading + outgoing - this is always safest, as then you're the only person with access to your mail.
This may sound like paranoia... until you research the death of the fantastic HushMail service...
Depending on your exact reasons, using a 3rd party is acceptable if you don't mind every Gov bureaucracy reading your mail.
If you require... complete security... run your own infrastructure... with all related services running on physical machines outside the US legal jurisdiction.
The US can still go after you... and... by taking the simple step of non-US servers, the cost of going after you goes from a phone call to some Big Tech Cartel Shill... to huge amounts of money dealing with non-US governments... pitching them to turn over your data...