It appears that Microsoft has released ,NET Core 1.1 and ASP.NET Core. There is a lot of information to absorb and understand.
Places you may want to start with:
There is so much information, samples, tutorials you can leverage in order to get up-to-speed on ASP.NET Core and .NET Core. I’m really only interested in the API, server centric of .NET Core and ASP.NET Core. I know ASP.NET Core has awesome SPA development support and also Native support of iOS, Android on the Mac. Before I make the move into looking at Microsoft native offering I will be focusing on Native using Swift and Xcode.