Higher dimensional minimal model program (HD MMP) Organised by Corti, McKernan and Reid The subject dates back to work of Mori, Kawamata, Reid, Shokurov and others in the late 1970s, but has seen tremendous progress since the 1990s; it formed a major component of our Newton Institute program in 2002, and is the subject of the forthcoming book of Corti and others. This work culminates in the recent announcement in results of [Birkar, Cascini, Hacon, McKernan] of the completion of important components of the (log) minimal model program in all dimensions. We intend to devote the first component of WAG07-08 to the developments and dissemination of these results, which by then should have matured. The solution to this long-standing series of conjectures opens up new research directions within Mori theory, as well as having many potential implications for existing problems of higher dimensional algebraic geometry, singularity theory and Diophantine geometry. This is a rich field of fruit ripe for the picking. We plan to run an introductory workshop in Sep 2007, a regular seminar during Sep--Dec 2007, and a major workshop with draft dates: Wed 12th--Thu 20th Dec 2007. HD MMP will also be involved in our concluding conference in Jul 2008, and there will be follow-up activities over the next few years. Participants. Confirmed: Birkar, Corti, Fujino, Hacon, Kawamata, Koll{\'a}r, McKernan, Reid, Takagi Targetted: Alexeev, Ambro, Caibar, Campana, Cascini, Cheltsov, Debarre, Ein, de Fernex, Hacking, Hassett, Lazarsfeld, Kawakita, Keel, Kovacs, Matsuki, Mella, Nikulin, Prokhorov, Pukhlikov, Shokurov, Toda, Totaro, Tziolas, Viehweg, Wilson, Wisniewski, Yasuda,