theorems in optimal control theory, and fixed point theorems in
ematical economics, usually does not understand that he/she is
tially studying the same things. And the student is led to st
basic topology individually. (An exceptional event, which appa
had a crucial influence on my generation of Moscow mathema
and, undoubtedly, on my own mathematical education, was th
cial (i.e., nonobligatory) topology course given by D. B. Fuchs
Mechanics and Mathematics Department of Moscow State Uni
For several years (in the late 80s and the early 90s), I g
formal introductory topology courses for undergraduates an
school students at specialized math schools. I would like to
the administration of the Independent University of Moscow
opportunity to give this course as part of the basic curriculum t
students in the second and third semesters in 1996.
I am also extremely grateful to V. V. Prasolov, who took do
lecture notes and carried out their initial editing, and to the d
of Phasis Publishers, V. V. Filippov, for his initiative and sup
The lecture note origins of the book left a significant impr
its style. It contains very few detailed proofs; I tried to give as
illustrations as possible and to show what really occurs in top
not always explaining why it occurs. As a rule, only those
(or sketches of proofs) that are interesting per se and have imp
generalizations are presented.
In conclusion, here is a list of suggested references.
 J. W. Milnor, Topology from the differentiable viewpoin
University Press of Virginia, Charlottesville, VA, 1965; Pri
Univ. Press, Princeton, NJ, 1997.
 A. H. Wallace, Differential Topology, W. A. Benjamin
 V. V. Prasolov, Intuitive Topology, American Mathem
Society, Providence, RI, 1995.
 C. Kosniowski, A First Course in Algebraic Topology,
bridge University Press, 1980.