This thesis, containing four sections. In the first section, functionalization of graphite was performed through Diels–Alder (DA) reaction, using maleimide as a functionalization agent, then it characterized by different methods. The as-obtained functionalized graphene show ultra-efficient hydrogen evolution reaction activity as a metal-free electrocatalyst with an overpotential of 391 mV (vs. RHE) to reach a current density of 10 mA cm -2 , with superior stability in alkaline medium and low cost. In the second section, a new composite material was reported based on urchin-like sphere arrays Co 3 O 4 and functionalized graphene in the first section by means of a one-pot hydrothermal strategy. The obtained nanocomposites was used for oxygen evolution reaction. Electrochemical studies show superior stability under alkaline conditions and exhibit an overpotential of 242 mV with a Tafel slope of 80 mA dec -1 . In the third section, Co 3 O 4 nanorod–functionalized graphene hybrid has been fabricated as a highly efficient electrocatalyst for water oxidation in alkaline electrolytes. The well-defined Co 3 O 4 nanorods were successfully anchored onto graphene modified with the ethylenediamine following a simple route. The as-prepared hybrid shows excellent electrocatalytic activity towards oxygen evolution reactions in 1.0 mol L -1 KOH. In addition, the fabricated catalyst exhibits prominent stability during long-term electrolysis of water. In the final section, the delamination of three-dimensional architectures graphite into two-dimensional graphene nanoplate with covalent functionalization, as revealed by the IR spectroscopy and XPS technique, confirmed the presence of sulfonic acid groups in sulfonated graphene (SG). Furthermore, the resulting edge SG could display not only a remarkable selectivity for oxygen reduction reaction via a four-electron pathway, but also outstanding stability and tolerance to methanol crossover with respect to platinum.