Though a few of the results presented are proved in the recent references provided, the way they are combined with others and patched together around the three books quoted is new. In view of the importance of the full paper, the present version is only a summary of the definitive version to appear later on. Finally, the reader must not forget that "each formula" appearing in this new general framework has been used explicitly or implicitly in (C), (M) and (W) for a mechanical, mathematical or physical purpose. This paper has now been published as a chapter of a book: J.F. Pommaret (2012). Spencer Operator and Applications: From Continuum Mechanics to Mathematical Physics", Continuum Mechanics - Progress in Fundamentals and Engineering Applications, Dr. Yong Gan (Ed.), ISBN: 978-953-51-0447-6, InTech, Available from: http://www.intechopen.com/books/continuum-mechanics-progress-in-fundamentals-and-engineering-applications/spencer-operator-and-applications-from-continuum-mechanics-to-mathematical-physics
