  During 2004, four divisions of the American Physical Society commissioned a
study of neutrino physics to take stock of where the field is at the moment and
where it is going in the near and far future. Several working groups looked at
various aspects of this vast field. The summary was published as a main report
entitled ``The Neutrino Matrix'' accompanied by short 50 page versions of the
report of each working group. Theoretical research in this field has been quite
extensive and touches many areas and the short 50 page report provided only a
brief summary and overview of few of the important points. The theory
discussion group felt that it may be of value to the community to publish the
entire study as a white paper and the result is the current article. After a
brief overview of the present knowledge of neutrino masses and mixing and some
popular ways to probe the new physics implied by recent data, the white paper
summarizes what can be learned about physics beyond the Standard Model from the
various proposed neutrino experiments. It also comments on the impact of the
experiments on our understanding of the origin of the matter-antimatter
asymmetry of the Universe and the basic nature of neutrino interactions as well
as the existence of possible additional neutrinos. Extensive references to
original literature are provided.
