A free, comprehensive guide to game mathematics in Unity3D.

• Chapter 1 — The Basics: local/global space, distances, clamping, percentages
• Chapter 2 — Vectors A to Z: movement, dot/cross products, MoveTowards, space conversion, debugging
• Chapter 3 — Quaternions A to Z: rotations, LookRotation, RotateTowards, orbit systems
• Chapter 4 — Tweening & Easing: Lerp, AnimationCurve, DOTween
• Chapter 5 — Physics Engine: Rigidbody, colliders, joints, CharacterController
• Chapter 6 — Physics Programming: AddForce, ForceMode, FixedUpdate, AddTorque
• Chapter 7 — Raycasting: Raycast, SphereCast, LayerMask, explosion forces
• Chapter 8 — Trigonometry: sine, cosine, Atan2, vector projection, turret controller
• Chapter 9 — Trajectories: ballistic math, LineRenderer arc preview, reverse targeting
• Chapter 10 — Transformation Matrices: Matrix4x4, TRS, GPU instancing

Each chapter includes step-by-step C# code examples and practical exercises.