Before showing the Table of contents of this book, we would like brie?y to explain our motivation to the subject. In the mid-eighties, J.-L. Lions c- tributed to the multiplier method by proving powerful and elegant theorems on observability, controllability, and uniform stabilization. His 1988 survey article and monograph also stimulated intensive research activity in the ?eld. Themultiplier method ledto greatsuccess,but severalproblemsremained unsolved. Starting research on them, we came up with another e?cient way to deal with those issues: using a former approach based on harmonic an- ysis. Indeed, following the in?uential survey paper of D.L. Russell (1978), many authors had emphasized a classical result of A.E. Ingham (1936) for its simplicity anddepth that hadprovento be extremely useful in controltheory. In this book, our purpose is to unify, as much as possible, the so-called harmonic (or nonharmonic) analysis method. It is also to make the subject as simple as possible. We start by solving elementary “ad hoc” controllability problems; then we extend the results and the proofs to a general framework. Thebookcontainsalmostallproofsofthetheorems,andonlylittleknowledge offunctionalanalysisisrequired.Manyresultspresentedherearenewandstill unpublished, while many known results have been rewritten for the purpose of simpli?cation.