This monograph is based on the Ph.D. Thesis of the author [58]. Its goal is twofold: First it presents most researchwork that has been done during his Ph.D. or at least the part of the work that is related with the joint spectral radius. This work was concerned with theoretical developments (part I) as well as the study of some applications (part II). As a second goal it was the author s feeling that a survey on the state of the art on the joint spectral radius was really missing in the literature so that the ?rst two chapters of part I present such a survey. The other chapters mainly report personal research except Chapter 5 which presents animportantapplicationofthejointspectralradius: thecontinuityofwavelet functions. The ?rst part of this monograph is dedicated to theoretical results. The ?rst two chapters present the above mentioned survey on the joint spectral radius. Its minimum-growth counterpart the joint spectral subradius is also considered. The next two chapters point out two speci?c theoretical topics that are important in practical applications: the particular case of nonne- tive matrices and the Finiteness Property. The second part considers applications involving the joint spectral radius.