本书自1968年出版后，就牢固地树立了其经典地位，并受到学生和专家们的推崇。Katznelson教授因此书而获得了2002年度的斯提奖。
本书从经典傅里叶分析的清晰表述入手，旨在用一个具体的构架展示调和分析的**思想，并提供了大量有助于透彻了解调和分析理论的例子。作者在确立这些思想之后，转向扩展调和分析，使之远远超越圆群的范围，并通过在实线上讨论傅里叶变换以及在局部紧阿贝尔群上对傅里叶分析的简单考察，打开通向其他领域的大门。
与以前的版本相比，本版增加了若干补充材料，其中包括逼近论中的诸多主题和在调和分析中运用概率论方法的一些例子。

Ⅰ Fourier Series on T
1 fourier coefficients
2 Summability in norm and homogeneous banach spaces on T
3 Pointwise convergence of σn(f)
4 The order of square summable functions
5 Fourier series of square summable functions
6 Absolutely convergent Fourier series
7 Fouries coefficients of linear functionals
8 Additional comments and aqqlications
9 The d-dimensional torus
Ⅱ The Convergence of Fourier Series
1 Convergence in norm
2 Convergence and divergence at a point
3 Sets of divergence
Ⅲ The Conjugate Function
1 The conuugate function
2 The maximal function of Hardy and Littlewood
3 The Hardy spaces
Ⅳ Interpolation of Linear Operators
1 Interpolation of norms and of lihear operators
2 The theorem of Hausdorff-Young
3 Marcinkiewicz's theorem
Ⅴ Lacunary Series and Quasi-analytic Classes
1 Lacunary series
2 Quasi-analytic classes
Ⅵ Fourier Transforms on the Line
1 Fourier transforms for L1(R)
2 Fourier-Stieltjes transforms
3 Fourier transforms in Lp(R),1<p</-2
4 tempered distributions and pseudomeasures
5 Almost-Periodic functions on the line
6 The weak-star spectrum of bounded functions
7 The Paley-Wiener theorems
8 The Fourier-Carleman transform
9 Kronecker's theorem
Ⅶ Fourier Analysis on Locally Compact A belian Groups
1 locally compact abelian groups
2 The Haar measure
3 Characters and the dual group
4 Fourier transforms
5 Almost-periodic functions and the Bohr compactification
Ⅷ Commutative Banach Algebras
……
A Vector-Valued Functions
B Probabilistic Methods
Bibliography
Index

“本书在具体材料与抽象概念之间取得了恰到好处的平衡，作者在选择*适宜的主题方面独具慧眼。对题材清晰而简练的阐述以及选用的大量练习，对于想要掌握这门学科基础的人来说无疑是理想的知识源泉。”——2002 Steele Prize Citation