This thesis describes the covalent modification of carbon electrodes with a monolayer of polymerisation initiators and the growth of polymer brushes by surface initiated atom transfer radical polymerisation (SI-ATRP). Monolayer modification was sought to preserve the underlying electrode properties and topography and to produce a well-organised layer from which the polymer brushes can be grown. This work investigated two approaches for immobilising a monolayer of polymerisation initiators. Firstly, the electrochemical grafting of protected aryl diazonium salts produced a covalently anchored monolayer of tether groups that can participate in subsequent amide coupling and click reactions, to covalently anchor the polymerisation initiator. Secondly, specific reactions between the electrode surface and appropriate polymerisation initiator derivatives have been used to covalently anchor the initiators. For most systems, electro-active ferrocene (Fc) groups were reacted with modified surfaces as model reactants to enable the electrochemical estimation of the surface concentration of the polymer initiator groups. Film thickness measurements of the ethynylaryl (Ar-Eth) monolayer were carried out using atomic force microscopy confirming a monolayer. XPS analysis confirmed the presence of bromine on most of the polymerisation initiator modified samples. Modification of surfaces with polymer brushes can introduce new surface properties, such as switchable wettability, while maintaining the underlying bulk substrate properties. This work focused on examining SI-ATRP at each of the polymerisation initiator monolayers, with the aim to identify the most promising system(s) for further investigation. Polymer brushes of poly(3-(methacryloylamino)propyl)-N,N’-dimethyl(3-sulfopropyl)-ammonium hydroxide) (PMPDSAH) were grown from initiators tethered through the aryl diazonium salts modification procedure. Redox probe voltammetry and XPS analysis indicated that the grafting from polymerisation by the copper catalysed SI-ATRP was successful. Polymer brushes of poly(methyl methacrylate) PMMA were grown from the Ar-Eth modified monolayer by three SI-ATRP procedures: a standard procedure, an electrochemically mediated SI-ATRP method and a one-pot copper catalysed azide-alkyne click (CuAAC) reaction and SI-ATRP reaction from the Ar-Eth monolayer. Redox probe voltammetry and AFM images provided evidence for the growth of polymer brushes by these three methods. The successful one-pot CuAAC/SI-ATRP reaction for simultaneous coupling of the polymerisation initiator to the surface and polymerisation is a new approach for the production of polymer brushes and it minimises the number of surface modification steps needed. This method appears most promising for further development.