The topics in this survey volume concern research done on the
differential geom- etry of foliations over the last few years. After a
discussion of the basic concepts in the theory of foliations in the
first four chapters, the subject is narrowed down to Riemannian
foliations on closed manifolds beginning with Chapter 5. Following the
discussion of the special case of flows in Chapter 6, Chapters 7 and 8
are de- voted to Hodge theory for the transversal Laplacian and
applications of the heat equation method to Riemannian foliations.
Chapter 9 on Lie foliations is a prepa- ration for the statement of
Molino's Structure Theorem for Riemannian foliations in Chapter 10. Some
aspects of the spectral theory for Riemannian foliations are discussed
in Chapter 11. Connes' point of view of foliations as examples of non-
commutative spaces is briefly described in Chapter 12. Chapter 13
applies ideas of Riemannian foliation theory to an infinite-dimensional
context. Aside from the list of references on Riemannian foliations
(items on this list are referred to in the text by [ ]), we have
included several appendices as follows. Appendix A is a list of books
and surveys on particular aspects of foliations. Appendix B is a list of
proceedings of conferences and symposia devoted partially or entirely to
foliations. Appendix C is a bibliography on foliations, which attempts
to be a reasonably complete list of papers and preprints on the subject
of foliations up to 1995, and contains approximately 2500 titles.
