In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods.

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused works.

I. Geometric Operators and the Inde.- Spectral invariants of operators of Dirac type on partitioned manifolds.- Index theory of Dirac operators on manifolds with corners up to codimension two.- Index defects in the theory of spectral boundary value problems.- Cyclic homology and pseudo differential operators, a survey.- Index and secondary index theory for flat bundles with duality.- II. Elliptic Boundary Value Problems.- Toeplitz operators, and ellipticity of boundary value problems with global projection conditions.- On the tangential oblique derivative problem - methods, results, open problems.- A note on boundary value problems on manifolds with cylindrical ends.- Relative elliptic theory.- Appendix. Fourier Integral Operators.- A.1. Homogeneous Lagrangian manifolds.- A.2. Local description of homogeneous Lagrangian manifolds.- A.3. Composition of homogeneous Lagrangian manifolds.- A.4. Definition of Fourier integral operators.- A.5. Pseudodifferential operators as Fourier integral operators.- A.6. Boundedness theorems.- A.7. Composition theorems.- References.