Foundations of Game Engine Development is a new book series currently being written by Eric Lengyel. Its four volumes cover the essentials of game engine development in the broad areas of mathematics, graphics, animation, and physics.
Volume 1: Mathematics Volume 1 book will begin with conventional treatments of topics such as linear algebra, geometry, and transforms. Then, it will introduce Grassmann algebra and geometric algebra to provide a much deeper understanding of the subject matter and highlight the places where traditional arithmetic with vectors, matrices, quaternions, etc., isn't quite correct. Below is a tentative table of contents listing most of the important topics that will be covered in the book. Each chapter will go into great detail and include extensive problem sets. Chapter 1: Vectors and Matrices
Chapter 2: Transforms
Chapter 3: Geometry
Chapter 4: Advanced Algebra

Volume 2: Graphics Below is a list of topics that are planned to be covered in the second volume.

Volume 3: Animation Below is a list of topics that are planned to be covered in the third volume.

Volume 4: Physics Below is a list of topics that are planned to be covered in the fourth volume.
