BezierKit is a comprehensive Swift library for constructing, manipulating, and computing with Bézier curves and paths. It provides linear, quadratic, and cubic curve types, along with advanced operations including curve-curve intersection (via monotone subdivision with implicitization fallback), offsetting, boolean operations (union, subtract, intersect), bounding box computation, nearest-point projection, arc length via Legendre-Gauss quadrature, and self-intersection removal. The library is designed for cross-platform use (macOS, iOS, Linux, WebAssembly) and includes a macOS demo application for interactive testing. The codebase demonstrates strong software engineering practices: protocol-oriented design, extensive unit tests (including adversarial edge cases), performance optimizations (concrete type overloads, stack allocation, manual memory management in hot paths), and a clean separation of concerns. While pre-release (semver < 1.0) with some known numerical edge cases documented as expected failures, the library is production-ready for vector graphics, CAD, and computational geometry applications.