This textbook describes the numerical calculation of nonlinearities in structural mechanics, i.e., large rotations, large deformations (geometric nonlinearities), nonlinear material behavior, particularly plasticity and time-dependent behavior, as well as contact. Building on this, stability problems and load calculations are addressed. The issues are explained using simple systems, formulated mathematically, integrated into the context of finite elements, and generalized to three dimensions. Each step is detailed, including numerical examples. This edition has been completely revised and expanded in the areas of mathematical methods, continuum mechanics representation, comparison of various concepts for large deformations, stability, and the arc length method. The contact chapter has been supplemented with Mortar-K.