This book is a self-contained introduction to fiber spaces and
differential operators on smooth manifolds that is accessible to
graduate students specializing in mathematics and physics. Over the
last 20 years the authors developed an algebraic approach to the
subject and they explain in this book why differential calculus on
manifolds can be considered as an aspect of commutative algebra.
This new approach is based on the fundamential notion of observable
which is used by physicists and it will further the understanding
of the mathematics underlying quantum field theory. The
prerequisites for this book are a standard advanced calculus course
as well as courses in linear algebra and algebraic structures.
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