This volume contains the proceedings of the conference "state and Frequency Domain Approaches to Infinite-Dimensional Systems". The aim was to bring together engineers and mathematicians working in the field of linear infinite-dimensional systems who are specialists in one or more of the following categories of mathematical approaches: semigroup approches, p.d.e. approaches, frequency domain approaches and syntheses of state-space and frequency domain approaches. Since these approaches use very different sophisticated mathematical techniques, it is unusual for a scientist to be expert in all of them. On the other hand, there different approaches all purport to address the same control problems for the same classes of linear infinite-dimensional systems. It is therefore important to compare and discuss the advantages and disadvantages of these different mathematical techniques. To help ameliorate the communication gab a series of introductory tutorial lectures were given by specialists in the above-mentioned fields. There were complemented by some key survey papers on more recent research, as well as by papers representing original research in these areas.