This is an introductory text dealing with a part of mathematics: modern differential geometry
and the theory of Lie groups. It is written from the perspective of and mainly for the needs
of physicists. The orientation on physics makes itself felt in the choice of material, in the
way it is presented (e.g. with no use of a definition–theorem–proof scheme), as well as in
the content of exercises (often they are closely related to physics).
Its potential readership does not, however, consist of physicists alone. Since the book
is about mathematics, and since physics has served for a fairly long time as a rich source
of inspiration for mathematics, it might be useful for the mathematical community as
well. More generally, it is suitable for anybody who has some (rather modest) preliminary
background knowledge (to be specified in a while) and who desires to become familiar in
a comprehensible way with this interesting, important and living subject, which penetrates
increasingly into various branches of modern theoretical physics, “pure” mathematics itself,
as well as into its numerous applications.