本書共有4卷，作者是世界公認的分析學大師。這套4卷集的經典名著以廣義函數論為框架，論述了與偏微分方程理論有關的經典分析和現代分析的核心內容。第4卷內容包括：拉格朗日分布和傅立葉積分算子、主型的偽微分算子、次橢圓算子、柯西問題的惟一性、譜漸近展開和長范圍散射理論等。

Introduction Chapter XXV. Lagrangian Distributions and FourierIntegral Operators Summary 25.1. Lagrangian Distributions 25.2. The Calculus of Fourier Integral Operators 25.3. Special Cases of the Calculus， and L2 Continuity 25.4. Distributions Associated with Positive Lagrangian Ideals 25.5. Fourier Integral Operators with Complex Phase Notes Chapter XXVI. Pseudo-Differential Operators of Principal Type Summary 26.1. Operators with Real Principal Symbols 26.2. The Complex Involutive Case 26.3. The Symplectic Case 26.4. Solvability and Condition (ψ) 26.5. Geometrical Aspects of Condition (P) 26.6. The Singularities in N11 26.7. Degenerate Cauchy-Riemann Operators 26.8. The Nirenberg-Treves Estimate 26.9.The Nrenberg-Treves Estimate26.10.The Singularites on One Dimensional Bicharacterstics26.11.A Semi-Global Existence TheoremChapter XXVII.Subelliptic OperatorsSummary27.1.Defintions and Main Results27.2.The Taylor Expansion of the Symbol27.3.Subelliptic Operators Satsfying(P)27.4.Local Properties of the SymbolChapter XXVIIII.Uniqueess for the Cauchy problemChapter XXIX.Spectral AsymptoticsChapter XXX.Long Range Scattering TheoryBibliographyIndexIndex of Notation