Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more comprehensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research.

Introduction
Chapter 1 Linear differential difference equations
1.1 Differential and difference equations
1.2 Retarded differential difference equations
1.3 Exponential estimates of x(， f)
1.4 The characteristic equation
1.5 The fundamental solution
1.6 The variation-of-constants formula
1.7 Neutral differential difference equations
1.8 Supplementary remarks
Chapter 2 Retarded functional differential equations: basic theory
2.1 Definition
2.2 Existence， uniqueness， and continuous dependence
2.3 Continuation of solutions
2.4 Differentiability of solutions
2.5 Backward continuation
2.6 Caratheodory conditions
2.7 Supplementary remarks
Chapter 3 Properies of the solution map
3.1 Finite-or infinite-dimensional problem
3.2 Equivalence classes of solutions
……
Chapter4 Autonomous and peridic processes
Chapter5 Stability theory
Chapter6 General linear systems
Chapter7 Linear autonomous equations
Chapter8 Linear periodic systems
Chapter9 Pertubed linear systems
Chapter10 Behavior near equilibium and periodic orbits for autonomous equations
Chapter11 periodic soultons of autonomous equations
Chapter12 Eqations of neutral type
Chapter13 Global theory
Appendix
Stability of charactersitc equations
Bibliography
Index