The book "Parametric Continuation and Optimal Parameterization in Applied Mathematics and Mechanics" offers a comprehensive analysis and further development of the parametric continuation method, originally introduced in the publication "Problems of Nonlinear Deformation." The authors, V. I. Shalashilin and E. B. Kuznetsov, present advancements in the application of this method to various mathematical and mechanical problems. The work demonstrates that a single algorithm for parametric continuation can be used not only to solve nonlinear problems with parameters but also for a wide range of other applications, including solving initial value problems for ordinary differential equations and curve interpolation. A key finding of the research is the realization that the arc length along the solution curve serves as an optimal continuation parameter. This book is divided into several chapters that address different classes of problems, showcasing the versatility of the method.