本书综述了Banach空间理论取得的相当大的进展，这是Grothendieck的奠基性论文《Re?umé de la théorie métrique des produits tensoriels topologiques》的结果。作者考虑的中心问题是Banach空间X和Y具有性质：每个从X到Y的有界算子都具有Hilbert空间分解，特别是当这些算子定义在Banach格、 代数或圆盘代数和 上时。他回顾了Grothendieck论文最后提出的六个问题，这些问题现在都已经解决了（除了Grothendieck常数的确切值），并包括这些问题解决过程中的各种结果。最后一章是作者对几个Banach空间的构造，使得内射张量积和射影张量积重合，这给了Grothendieck第六问题一个否定的解决方案。 尽管本书的读者对象是从事泛函分析、调和分析和算子代数等领域研究的数学家，但是本书详细和完备的处理使具有泛函分析基础的非专业人士也能够阅读。事实上，作者特别关注的是最近对Banach空间几何的研究成果，特别是它们如何应用于其他领域，如调和分析和 代数。

前辅文
Chapter 0. Preliminary Results and Background
  a. General notation
  b. An introduction to tensor products. The approximation property. Nuclear operators
  c. Local reflexivity
Chapter 1. Absolutely Summing Operators and Basic Applications
  a. Absolutely summing operators
  b. Applications to Banach spaces
  c. An introduction to duality theory. Integral operators
  Notes and references
Chapter 2. Factorization through a Hilbert Space
  a. Operators factoring through a Hilbert space
  b. A duality theorem
  Notes and references
Chapter 3. Type and Cotype. Kwapieh's Theorem
  a. Type and cotype. Definitions
  b. Kwapieh's theorem
  c. Supplementary results
  d. Type and cotype and the geometry of Banach spaces
  Notes and references
Chapter 4. The "Abstract" Version of Grothendieck's Theorem
  a. The factorization theorem
  b. An application to harmonic analysis
  Notes and references
Chapter 5. Grothendieck's Theorem
  a. Preliminaries. Localization techniques. J^-spaces
  b. Operators on C( K )-spaces
  c. Operators on Lj-spaces
  d. Cotype 2 spaces and absolutely summing operators
  e. Best constants. Krivine's proof
  f. A proof of G.T. using harmonic analysis
  Notes and references
Chapter 6. Banach Spaces Satisfying Grothendieck's Theorem
  a. G.T. spaces
  b. G.T. spaces of cotype 2
  c. Quotients of Ll by a reflexive subspace
  d. Bourgain's theorem on Lx/Hl
  Notes and references
Chapter 7. Applications of the Volume Ratio Method
  Notes and references
Chapter 8. Banach Lattices
  a. The Banach lattice version of G.T.
  b. Ultraproducts. Factorization through an L^-space
  c. Local unconditional structure. The Gordon-Lewis property
  d. Examples of Banach spaces without l.u.st.
  e. Finite-dimensional spaces with extreme l.u.st. constants
  f. G.T. spaces with unconditional basis
  g. Infinite-dimensional Kasin decompositions
  Notes and references
Chapter 9. C *-Algebras
  a. The noncommutative version of G.T.
  b. Applications
  Notes and references
Chapter 10. Counterexamples to Grothendieck's Conjecture
  a. Outline of the construction
  b. Extensions of a Banach space
  c. The construction
  d. Particular cases of the conjectures
  e. Some open problems
  Notes and references
References