Hector O. Fattorini graduated from the Licenciado en Matemática, Universidad de Buenos Aires in 1960 and gained a Ph.D. in Mathematics from the Courant Institute of Mathematical Sciences, New York University, in 1965. Since 1967, he has been a member of the Department of Mathematics at the University of California, Los Angeles.

Review of the hardback: '… very well conceived and organised with a good selection of material and an excellent combination of detail and perspective … It should serve well as the standard reference'. Bulletin of the London Mathematical Society

• Editor's statement; Foreword; Preface; 1. Elements of functional analysis; 2. The caucy problem for some equations of mathematical physics: the abstract cauchy problem; 3. Properly posed cauchy problems: general theory; 4. Dissipative operators and applications; 5. Abstract parabolic equations: applications to second order parabolic equations; 6. Perturbation and approximation of abstract differential equations; 7. Some improperly posed cauchy problems; 8. The abstract cauchy problem for time-dependent equations; 9. The cauchy problem in the sense of vector-valued distributions; References; Index.