An entire generation of mathematicians has grown up during the time -
tween the appearance of the ?rst edition of this textbook and the
publication of the fourth edition, a translation of which is before you.
The book is fam- iar to many people, who either attended the lectures on
which it is based or studied out of it, and who now teach others in
universities all over the world. I am glad that it has become accessible
to English-speaking readers. This textbook consists of two parts. It is
aimed primarily at university students and teachers specializing in
mathematics and natural sciences, and at all those who wish to see both
the rigorous mathematical theory and
examplesofitse?ectiveuseinthesolutionofrealproblemsofnaturalscience. The
textbook exposes classical analysis as it is today, as an integral part
of Mathematics in its interrelations with other modern mathematical
courses such as algebra, di?erential geometry, di?erential equations,
complex and functional analysis.