  Fourier Transforms is a first in a series of monographs we present on
harmonic analysis. Harmonic analysis is one of the most fascinating areas of
research in mathematics. Its centrality in the development of many areas of
mathematics such as partial differential equations and integration theory and
its many and diverse applications in sciences and engineering fields makes it
an attractive field of study and research.
  The purpose of these notes is to introduce the basic ideas and theorems of
the subject to students of mathematics, physics or engineering sciences. Our
goal is to illustrate the topics with utmost clarity and accuracy, readily
understandable by the students or interested readers. Rather than providing
just the outlines or sketches of the proofs, we have actually provided the
complete proofs of all theorems. This will illuminate the necessary steps taken
and the machinery used to complete each proof.
  The prerequisite for understanding the topics presented is the knowledge of
Lebesgue measure and integral. This will provide ample mathematical background
for an advanced undergraduate or a graduate student in mathematics.
