Lankoski, P., Holopainen, J. (2017). Game design research - An introduction to theory & practice. ETC Press.
This is a comprehensive introduction into Game Design research and also available for free! https://press.etc.cmu.edu/index.php/product/game-design-research/
Also, I compiled a list of game design and other related textbooks for personal use here: https://www.notion.so/Game-Design-Education-11244d214b824c13af8ce5ab6bc6a4b6
Seconding Afsaneh Yadaei , The art of game design is truly excellent, I would consider this as the best entry point into game design theory. If you are completely new to game development, Level up! might be a better start, though from what I've heard it is very basic.
We just published a review on theoretical foundations in scientific research on gamification, serious games and game-based learning: https://doi.org/10.1016/j.chb.2021.106963 It is still in press, but I can share the manuscript if you don't have institutional access :)