The training objective of the project is to educate through research in analysis and mathematical physics top young scientists in this area. The network plans to organize two summer schools for two incoming generations of postdocs (estimating that each team will have two successive persons). These will enable the new postdocs to get acquainted with the state-of-the-art in the field, the tasks to be performed, and with the scientists in the other teams. The network provides teams with a proven track record in research and experienced team leaders. The teams will conduct weekly seminars and offer special lectures relevant to the tasks to be performed. The young postdocs will be encouraged to participate. To exploit the networking potential the network will encourage short and long term visits between the teams collaborating on the same task.