You will need an editor to write the code, a terminal to compile the code, and a browser to see the results. Visual Studio Code and Atom with atom-typescript are good editors in which you can write TypeScript code. These are available for Windows, Mac, and Linux. You have to compile TypeScript in a terminal. On Windows, you can use the Command Prompt or Powershell for that. On a Mac, you can use Terminal.
To compile TypeScript, you need NodeJS. You can find details on how you can install it in the first chapter.
Chapter 5, Native QR Scanner App, has more requirements to run the mobile app in an emulator or a device. Details about how you can install these dependencies are found in the chapter.