concepts as needed. Apart from the well–known conformal and projective struc-
tures, the book contains extensive material on almost Grassmannian structures, al-
most quaternionic geometries, CR–geometries and Lagrangean contact geometries,
quaternionic contact geometries, low–dimensional distributions, path geometries,
and many others. This includes part of their twistor theory, correspondence spaces
and further functorial constructions.
Readers familiar with differential geometry and Lie theory, who are interested
in the general approach to parabolic geometries might prefer to look at the “Pro-
logue” 1.1 in order to get a sense for the typical examples of the structures in
question, inspect briefly the generalities on Cartan connections in 1.5 and then be-
gin a serious reading straight from Chapter 3. If necessary, it should be possible to
find background material, concepts and technicalities quickly in Chapters 1 and 2.
Finally, both Chapters 1 and 2 are also intended to be useful as a broader
introduction to the subject and have been used successfully as underlying material
for various graduate courses, both in Vienna and Brno. Thus we also believe that
readers at the graduate student level may enjoy reading the book in the order it is
written, with possible glimpses backward and forward for illustrations of the general
considerations as they go.
Acknowledgement. Although we heard that delays are common with math-
ematical books, the work on this one certainly has taken much longer than anyone
expected, and we are grateful to the publisher for his patience and support during
all of these years. We would also like to mention here many of our collaborators
and colleagues who contributed countless suggestions and comments during the ten
years of the development of this project. Our particular thanks are due to those
colleagues and students of ours who attended our seminars in Vienna and Brno,
where most of the contents of this first volume of our book was read, presented and
discussed in detail the project could hardly have been accomplished without
their efforts.
Vienna and Brno, August 20, 2008
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