Most JavaScript code relies on functionality implemented by the numerous JavaScript libraries and frameworks available, such as jQuery.
To use these libraries from Typescript, you can either create so-called ambient definitions for the JS library manually, or use existing Typescript definition files (extension .d.ts).
The TypeScript source code repository contains a jquery.d.ts in the /bin directory, and a definition file for jquery.ui can be found in /samples/warship. However, those samples need not cover the respective library completely.
This question on SO points us to the github repository DefinitelyTyped
TypeScript type definitions repository for popular JavaScript libraries.
The project aims to provide high quality definitions for the most popular libraries out there.
which lists about 50 definition files covering major JS libraries and frameworks.