The volume is aimed at researchers and graduate students interested in theoretical and computational problems in geometric integration theory, nonlinear control theory, and discrete mechanics.

Preface.- A. Iserles and G.R.W. Quispel, Why geometric numerical integration?.- B. Owren, Lie group integrators.- H. Z. Munthe-Kaas and K. K. Føllesdal, Lie-Butcher series, Geometry, Algebra and Computation.- A. Murua and J. M. Sanz-Serna, Averaging and computing normal forms with word series algorithms.- L. A. Duffaut Espinosa, K. Ebrahimi-Fard, and W. Steven Gray, Combinatorial Hopf algebras for interconnected nonlinear input-output systems with a view towards discretization.- F. Casas, Computational aspects of some exponential identities.- K. Ebrahimi-Fard and I. Mencattini, Post-Lie Algebras, Factorization Theorems and Isospectral Flows.- G. Bogfjellmo, R. Dahmen, and A.Schmeding, Overview of (pro-)Lie group structures on Hopf algebra character groups,.- M. Barbero Liñán and D. Martín de Diego, Bäcklund transformations in discrete variational principles for Lie-Poisson equations.- M. Vermeeren, Numerical precession in variational discretizations of the Kepler problem.- O. Verdier, Full affine equivariance and weak natural transformations in numerical analysis - the case of B-Series.- References.