It is very much possible that most people are still using Visual Studio 2013 at their work as normally enterprises take their time to evaluate and approve new version of any products. If you are one of them and planning to learn and build new Angular2 application, be aware you cannot use same IDE. Why?
Having said that, TypeScript version 2.0+ is one of the prerequisites for building Angular2 applications and surprisingly the team have decided to not support TypeScript 2.0 in Visual Studio 2013. There is no official communication, blog post or tweet about this decision from Microsoft except someone responded for this issue in GitHub. The last supported TypeScript version for Visual Studio 2013 is 1.8. Alternatively, you can use Visual Studio Code for building several types of Web applications including Angular2 and you don’t have to wait till you get Visual Studio 2015.
Visual Studio Code is out there to rescue you. It is completely free, lightweight, cross platform, web development centric, provides most features of its big brother (Visual Studio) such as navigation, IntelliSense, debugging, source control integration, plug-in support, customization, and so on. In fact, it is an ideal choice for Angular2.
If you are working or exploring on your personal machine and prefer to stay with Visual Studio, you can use the Visual studio 2015 Community edition which is equivalent to professional edition and free for developers and startups with small teams.