Nonlinear dynamics is a fascinating rapidly growing field in research and applications. Almost everywhere in nature one encounters beautiful dynamical phenomena which are challenging to understand. New phenomena have been found in physical experiments and in extensive numerical simulations. Engineering problems currently being investigated are for example self-excited vibrations of rotor systems, dynamics of wind turbines, granular dynamics, fluid-structure interaction, vibro-impacts, elastic waves in nonlinear media and many other fields. Numerics and algorithmic tools can however only be effective when joined with qualitative insight to understand the underlying generic mechanisms. A wealth of analytical and semi-analytical methods and techniques are available for the investigation of nonlinear systems. Many of them are classical, such as perturbation theory, others are of more recent origin. Examples of analytical methods for the investigation of ordinary and partial differential equations, which commonly arise in the context of nonlinear oscillations, are center manifold and normal form theory, nonlinear normal mode analysis and embedding techniques, such as Carleman linearization, among others. The major challenges are for example the study of bifurcations, the estimation of basins of attraction and the detection of chaotic behavior. The methods have to be adapted to different systems which may have slow and fast dynamics, as well as discontinuities yielding stiff differential equations. The aim of the planned symposium is to bring together leading scientists in applied mathematics, mechanics and engineering science, to further develop the analytical and semi-analytical methods in nonlinear dynamics, with a particular focus on mechanical systems described by ODEs, and PDEs and to explore their potentials and limitations. It is expected that in the future analytical, semi-analytical and numerical methods will be more commonly used for the solution of engineering problems, providing robust solutions and useful insights. The symposium is expected to contribute to finding such solutions and to compare different solution strategies.