This book discusses unconstrained optimization with R-a free, open-source computing environment, which works on several platforms, including Windows, Linux, and macOS. The book highlights methods such as the steepest descent method, Newton method, conjugate direction method, conjugate gradient methods, quasi-Newton methods, rank one correction formula, DFP method, BFGS method and their algorithms, convergence analysis, and proofs. Each method is accompanied by worked examples and R scripts. To help readers apply these methods in real-world situations, the book features a set of exercises at the end of each chapter. Primarily intended for graduate students of applied mathematics, operations research and statistics, it is also useful for students of mathematics, engineering, management, economics, and agriculture.