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ASP.NET Core
ASP.NET Core is a cross-platform .NET framework for building modern cloud-based web applications on Windows, Mac, or Linux.
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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
Most of basic .NET itself is almost identical to .NET Framework, with few new methods here and there. You can just switch framework and start coding. New language features are not at all essential and required to use, so you can just read C# release notes on MSDN, and start using them at your own pace. ASP.NET changed a lot, but for competent Framework developer, just reading through MSDN docs on new ASP.NET + doing some WebApi project is enough to get the gist of it. Stop hesitating and just go for it.