This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization - theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems - and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find:* More than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics.* Several subjects not typically found in optimization books - for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares.* A large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat-Weber problem, denoising, clustering, total least squares, and orthogonal regression.* Theoretical and algorithmic topics demonstrated by the MATLAB toolbox CVX and a package of m-files that is posted on the book's web site.