Recommended learning path for game development and design
If you are interested in game development and design you are in good luck because there are several free online courses:
Step 1) Start here: Serious Gaming (https://www.coursera.org/learn/serious-gaming) - This will give you an overview of the gaming industry. It is easy so just watch it for background. Don’t waste too much time here, because you will gain more from the second step below...
Step 2) Second, do a general course on game design, in other words learn how to think of and develop the rules for a game that will be fun to play. Do one or more of the following courses: I especially recommend you to do this course because it is the only course where you can get a certificate without paying any money, and it provides an excellent overview of game design: Concepts in Game Development (https://www.open2study.com/courses/concepts-in-game-development). This also provide an excellent overview: Introduction to Game Design (https://www.edx.org/course/introduction-game-design-mitx-11-126x-0).
Step 3) Game Design: Art and Concepts Specialization (https://www.coursera.org/specializations/game-design) - This course on Coursera teaches the arty and creative part of game development (I dont say with this statement that the programming part is less creative at all because programming is also highly creative but more technical or difficult). It is easy so do go through it. It will take some time because this is a bundle of 4 courses (ignore the last capstone project, this is only for if you pay to get a certificate).
Step 4) Game Design and Development Specialization (https://www.coursera.org/specializations/game-development) - This course on Coursera teaches the more business and technical aspects of game development. It will take some time because this is a bundle of 4 courses (ignore the last capstone project, this is only for if you pay to get a certificate) and it goes into programming. If you struggle with the programming you may want to do the next course (Beginning Game Programming with C#) before this one.
Step 5) Beginning Game Programming with C# (https://www.coursera.org/learn/game-programming) - This is an excellent course on Coursera that will learn you to develop games in the very popular game development platform Unity, using the very powerful and in-demand programming language called C#. This course is so good that after you completed it you will be able to write some quite advanced software other than games as well. I strongly recommend you to do this one after you worked through simpler courses mentioned above because this one is quite long and difficult, but definitely worth it.
After you have done the above free courses you will be able to develop advanced games - without paying any course fees!
For game development it important to get a good background in:
Graphic design: This field is going digital and there is no way to avoid that, so programming and software skills described above is also important for graphic design. Most graphic designers work in web or game development or at least use computer programs to make their designs therefore it is important to become very well familiar with computers and preferably some programming as well. Graphic designers who know web programming basics are more likely to get a job. If you want to stick for now only to the art side rather than computer side of graphic design (which i don't recommend), start with the Coursera platform. Simply click on "Catalog" to search for courses, then type in "graphic design". A lot of courses appear, then you can choose the one you want to start with. Coursera also have excellent courses on game design. FutureLearn have this important course since colour theory is very important in graphic design: www.futurelearn.com/courses/power-of-colour. LinkedIn Learning (this is the only one that is not really freely accessible) also have excellent courses on Graphic Design and design of icons.
Gamification is not the same as game development. It is about making real world work or activities more fun by building elements of gaming into it so that people are more motivated to do a boring job or some other dull task. If you do want to learn about it, Coursera has a really excellent, fun and easy course on this: https://www.coursera.org/learn/gamification
Virtual reality is the direction that gaming will move to, very quickly. This is more advanced and to enter this field first learn to develop normal games and to program as explained above. The same applies to Internet of Things (IoT), which is the connection of anything to sensors, motors, computers and the internet - this is also becoming more important in everything, including game development.
Game theory is not at all the same as game development, definitely do not start with this, this is a field that study human behaviour in general, and have lots of advanced maths.