As a new game designer, it can be challenging to find resources to enter the game design field if you're not already enrolled in college or some other technical training program. This is especially true if, like most independent developers, you are already working a regular job and trying to pursue your game design passions on the side. For people on a budget that cannot afford schooling or are maybe just dipping their toes into what being a game designer might be like, I would recommend the following reading materials as a stepping off point in this venture.
The Art of Game Design: A Book of Lenses by Jesse Schell
For some game designers, this book is required reading to start the journey as a game designer. While that sounds scary, Schell's Art of Game Design is very beginner friendly and rather encouraging for people new to the art form. Schell's book is a crash course of the various elements of game design as a subject of study and patiently guides the reader through the process by adding new elements one by one with each chapter. The most useful tools that he offers to new designers are his numerous lenses. Throughout the book, he will present the reader with questions related to the topic at hand that can be employed when in the process of designing a game. These questions are meant to pull the reader out of their own perspective and into the frameworks of various other things whether that is the essential experience of the game, the player's mind, or mechanics like time, space or rules. The lenses are extremely valuable when trying to problem solve or ideate some element of a game. Schell also leaves various resources and references throughout his work so that the reader can further explore certain topics that fascinate them or could use more elaboration. While the book's teachings could overall be better employed in a video game context, most of the principles laid out in this work can be applied effectively to both analogue and digital game design. The book is a bit pricy, but can be bought used or as a pdf for a much lower price.
Here's a link to a site containing all of Schell's lenses for free: https://deck.artofgamedesign.com/#/
Here's a link to the book itself on Schell's website:
Kobold's Guide to Board Game Design edited by Mike Selinker
Unlike the previous work, Kobold Guide to Board Game Design is explicitly about board games and is a collection of essays written by various game designers. The book takes the reader from the initial phases of having an idea for a board game all the way through getting the game published and sold at retailers. It is quick read, clocking in at 144 pages in total. There are essays in this book from such designers as Richard Garfield (Creator of Magic: The Gathering, King of Tokyo), Dale Yu (developer of Dominion), Andrew Looney (Fluxx), and Steve Jackson (GURPS, Munchkin). Each author takes a particular aspect of the designing, developing, or publishing process and breaks it down in an easy to understand and sagely manner. The book's core strength is its multidimensionality and how the perspective of each author intermingles to create a thorough analysis of the board game design process. While I have only read the first edition, there is a second edition that combines both the essays of the first edition with some new ones to better reflect the current board game landscape. Either edition is a fine book to pick up and both are reasonably priced for the amount information they contain.
Here's a link to the book on Kobold Publishing's website: https://koboldpress.com/kpstore/product/kobold-guide-to-board-game-design/?gad=1&gclid=CjwKCAjw-7OlBhB8EiwAnoOEk7w1tFBZpcnZvC-9uu4X26p-kIo4s2fitGO0ixDnVIDJjeB8M31UsxoCWngQAvD_BwE
The Ultimate History of Video Games by Steven L. Kent
Despite its title that is straight out of You-Tube thumbnail, The Ultimate History of Video Games is a rather all-encompassing work that takes the reader through the history of games from the early days of pinball in the 20s to around the release of the PlayStation 2. Of all the books on this list, this is probably the one that will feel the most like homework to read, especially if you're not into history. As a new designer, it provided me some valuable insight into the origins of the video game industry and how it has shaped our business to this day. A lot of the business principles that informed the amusement industry in the early 1900s have stuck around and are pillars of modern video game marketing. Also, learning about how the video game market crash of 1983 came about and what companies did afterward to respond was important to contextualize a lot the decisions video game companies made in the late eighties and early nineties. For example, the NES was released with the Zapper and R.O.B. to market it as a toy rather than a video game home console because no retailers were accepting video games into their stores due to the crash. The book is an easy read in terms of language, but it is around 550 pages long, so it is a bit of a sit. It is reasonably priced and can probably found in most libraries or online used for cheap.
Here's a link to the book on Penguin Random House Publishing's website: https://www.penguinrandomhouse.com/series/UHV/ultimate-history-of-video-games
Building Blocks of Table Top Game Design: An Encyclopedia of Mechanisms by Geoffrey Engelstein and Isaac Shalev
Once again, Building Blocks of Table Top Game Design: An Encyclopedia of Mechanisms is for meant analogue game design, but some of the mechanics found in this book can be applied in digital game design. Also, this book is explicitly for reference and does not give the reader instruction or insight as exactly to where, why, or when to employ these various mechanics. Despite that its value is in the sheer number of mechanics it lists out for designers. There are very few books like it that actually just list out the mechanics for the designer to reference. It is full of diagrams, examples, and descriptions about any given variant of the mechanic of a chapter. It is over 500 pages in length and exists for the sole purpose of answering niche questions about specific mechanics found in board games and how they function. It is an academic text and, as a result, has some dry, technical language with a steep price for physical copies. In terms of pricing as a digital read, it is much cheaper, an almost ninety percent drop in price, so I would recommend that version, especially as its value is mostly found in pulling it out on occasion to help problem solve. But when problem solving for mechanics, you're not going to find a more thorough book to help assist you.
Here's a link on CRC Press's website: https://www.routledge.com/Building-Blocks-of-Tabletop-Game-Design-An-Encyclopedia-of-Mechanisms/Engelstein-Shalev/p/book/9781032015811
A Theory of Fun for Game Design by Raph Koster
Koster's A Theory of Fun for Game Design is one of the most insightful books one could find on game design one could find as a new designer looking to find the spark behind an addicting game. This book is about the idea of 'fun' and where it comes from in games and how game designers can create games that are 'fun' for people to play. Despite its short length, Koster creates a compelling argument that games are a system of problems and the fun in them comes from the task of problem solving. He uses both text and illustrations to better explain his ideas to the reader, so this book is great if you have some difficultly with long-form explanations exclusively through text. A lot of his ideas about fun I find personally useful in my design work and employ them almost unconsciously at this point. For example, I now think about games in the framework of a problem in a controlled system presented to the player and the mechanics of the game are tools the player has to solve that problem and that the fun the player has in the system of a game is using the various tools provided to resolve the problem. It's one of those books that makes the brain think on it over and over again without realizing. As for pricing, this book can be found used online for relatively cheap.
Here's a link to the book on Koster's website: https://www.theoryoffun.com/
I would like to conclude by saying that these are not the five most important books for learning game design. They are useful jumping off points but they are in no way the only books you will read on the subject or studying you will have to do in order to become a game designer. In truth, the best way to become better at game design is consistently working on games by yourself or with others in a team. Books on the subject of games and game design are great ways to help guide your process but should not overtake your own instincts about what you find fun and enjoyable. They are attempts at finding what lies underneath the hood of games, but it isn't an exact science. Often the best tools found in these works are all of the various pieces of advice that give the perspectives of game designers and how they approach specific tasks. Take the pieces of advice that work best for you.