The dotnet repository is the starting point to engage in and learn about .NET open source projects from Microsoft and the .NET Foundation. You can read the more detailed .NET Core is Open Source on the .NET blog.
There are many open source .NET projects. Check out the list of projects the community maintains. Please find one to engage in or add one. There's certainly one out there that could use your help.
There are several projects from Microsoft on GitHub and CodePlex, including:
Each one of these projects maps to one or more .NET NuGet packages that are published on NuGet.org.
There are also many great open source .NET community projects, such as:
.NET open source projects from Microsoft (gladly) accept PRs and other contributions. To contribute to ASP.NET 5 or EntityFramework, see the ASP.NET Contributing Guide. To contribute to .NET Core 5, see the .NET Core Contributing Guide.
You are also encouraged to start a discussion by posting on the .NET Foundation Forums or filing an issue in the corresponding GitHub project. See the contributing guides for more details.
Most .NET open source projects at Microsoft have been contributed to the .NET Foundation. There are two main .NET Foundation projects for Microsoft open source projects: ASP.NET Core 5 project and the .NET Core 5 project.
.NET open source projects typically use either the MIT or Apache 2 licenses for code. Some projects license documentation and other forms of content under Creative Commons Attribution 4.0. See specific projects to understand the license used.