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The framework has many build-in tools, and many packages have been written targeting the framework.
Pro Cross platform
.Net Core can work on any platform.
Pro Widely used
It's pretty easy to find a job with it and there's plenty of documentation and tutorials around.
Pro Extensive documentation
There are a lot of resources available to get help.
Asp.NET Core on Linux is fast accordingly to TechEmpower benchmarks.
Pro Asp.NET core provides balance between magic/agility and craftsmanship
You can get ordinary details quickly but with complete freedom to make your craft, knowing everything that is happening underneath the cloths. The highly modular system makes it possible to scale small applications to large ones with ease.
Pro It has more users than any other backend web framework
Getting your next contract is easy with this on your CV.
Con Core and full ASP.NET are bit confusing sometimes
While not in feature parity (yet) they are still apart and support sometimes funky combinations of features - full ASP.NET has all the bells and whistles but doesn't offer cross platform so you may have to do some research what you really need. That being said, it got a lot better in 2.0.
You need to have the plate to maintain a site.