Textbook, MCCME, Moscow, 2000, 300 pp., ISSBN 5-900916-57-X
(in Russian).

The book is available at the Independent
University of Moscow (B. Vlasijevskij 11, bookstore at the ground floor,
for details and to order click
here) and at the
FizMatKniga Web-Shop.
The second (electronic) edition is now available on-line.
In this edition (likewise English one) new exercises were added (mostly)
to the first half of the book, thus achieving a better balance with
the second half. Besides, some typos
and minor errors, noticed in the first edition, were corrected.
Contents

Foreword

Chapter 1

Introduction

Chapter 2

Special smooth functions on R^{n}

Chapter 3

Algebras and points

Chapter 4

Smooth manifolds (algebraic definition)

Chapter 5

Charts and atlases

Chapter 6

Smooth maps

Chapter 7

Equivalence of coordinate and algebraic definitions

Chapter 8

Spectra and ghosts

Chapter 9

Differential calculus as an aspect of a commutative algebra

Chapter 10

Smooth bundles

Chapter 11

Vector bundles and projective modules

Afterword

Appendix. A. M. Vinogradov

The observability principle, the set theory, and
"foundations of mathematics"