Memoirs of the American Mathematical Society 2012; 217 pp; softcover Volume: 219 ISBN10: 0821869256 ISBN13: 9780821869253 List Price: US$88 Individual Members: US$52.80 Institutional Members: US$70.40 Order Code: MEMO/219/1031
 In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the \(m\)th elliptic integrable systems associated to a \(k^\prime\)symmetric space \(N=G/G_0\). The author describes the geometry behind this family of integrable systems for which we know how to construct (at least locally) all the solutions. The introduction gives an overview of all the main results, as well as some related subjects and works, and some additional motivations. Table of Contents  Introduction
 Notation, conventions and general definitions
 Invariant connections on reductive homogeneous spaces
 \(m\)th elliptic integrable system associated to a \(k^\prime\)symmetric space
 Finite order isometries and twistor spaces
 Vertically harmonic maps and harmonic sections of submersions
 Generalized harmonic maps
 Generalized harmonic maps into \(f\)manifolds
 Generalized harmonic maps into reductive homogeneous spaces
 Appendix
 Bibliography
 Index
 List of symbols
