As the range of phenomena that need to be simulated in engineering practice broadens, the limitations of conventional computational methods, such as finite elements (FE), finite volumes or finite difference methods, have become apparent. There are many problems of industrial and academic interest which cannot be easily treated with these classical methods. To overcome the limitations of classical methods, several advanced discretization techniques (mesh-free methods, extended/generalized FE or Dicontinuous Galerkin methods) have recently become very popular in the research community. However, despite their high potential and the important effort devoted to them in the last decade, advanced techniques require still very much attention to reach the popularity of conventional techniques for industrial applications. In fact, engineers are usually not trained in these techniques. The purpose of the ITN research project is to advance in the development and analysis of advanced techniques, with special attention to particular industrial applications of interests in the framework of computational mechanics. However, the introduction of new techniques in industry is only possible if industrial researchers have a deep knowledge and confidence on these techniques and are aware of their advantages. The ITN training program is addressed to researchers that, in the future, may be incorporated in industry. It is based on training-through-research with individual research projects, active participation in network activities and a wide offer of specific courses. In present, the network partners have a wide offer of training courses (joint Erasmus Mundus Master of Science in Computational Mechanics, etc). No experienced researchers or visiting professors are considered in this proposal. The dimension of the academic network teams and the scientific production of all of them clearly demonstrate that they are able to carry out the planned training program.