Let's use this thread to post high quality online courses on game design.
Introduction to Game Development
https://www.coursera.org/learn/game-development
Game Development for Modern Platforms
https://www.coursera.org/learn/gamedev-platforms
Introduction to Game Development
https://www.coursera.org/learn/game-development
If you love games and want to learn how to make them, then this course will start you down that path. Making games is a creative and technical art form. In this course you will familiarize yourself with the tools and practices of game development. You will get started developing your own videogames using the industry standard game development tools, including the Unity3D game engine and C#. At the end of the course you will have completed three hands-on projects and will be able to leverage an array of game development techniques to create your own basic games. This course is for individuals interested in becoming a game designer, game artist, or game programmer.
Game Development for Modern Platforms
https://www.coursera.org/learn/gamedev-platforms
The device or "platform" that a game is developed for and played on has a massive impact on the game development process. In this hands-on course you will explore how to develop a game for a variety of modern platforms, including Web, Windows, Mac OS X, iOS, and Android. While building a complete game, you will learn intermediate and advanced game development techniques in the Unity game engine. By the end of the course, you will understand how to develop, refine, package, and prepare your game for distribution on a variety of game platforms. Particular attention will be given to developing a 2D platformer game that supports multiple forms of input (keyboard/mouse, controller, and touch), works across multiple forms of output (screen size, screen resolution, sound), and performs well on a variety of computing devices.