We present exemplary results of extensive studies of mechanical, electronic, and transport properties of covalent functionalization of graphene monolayers (GML) with –NH2. We report new results of ab initio studies of covalent functionalization of GML with –NH2 groups up to 12.5% concentration. Our studies are performed in the framework of the density functional theory (DFT) and non-equilibrium Green's function (NEGF). We discuss the stability (adsorption energy), elastic moduli, electronic structure, band gaps, and effective electron masses as a function of the density of the adsorbed molecules. We also show the conductance and I(V) characteristic of these systems. Generally, the stability of the functionalized graphene layers decreases with the growing concentration of attachments and we determine the critical density of the molecules that can be chemisorbed on the surface of GLs. Because of local deformations of GLs and sp3 rehybridization of the bonds induced by fragments, elastic moduli decrease with increasing number of groups. Simultaneously, we observe that the functionalizing molecules stretch the graphene's lattice, the effect being more pronounced for higher concentration of adsorbed molecules. We find out that the GLs functionalization leads in many cases to the opening of the graphene band gap (up to 0.5302 eV for 12.5% concentration) and can be therefore utilized in graphene devices. The new HOMO and LUMO originate mostly from the impurity bands induced by the functionalization and they exhibit parabolic dispersion with electron effective masses comparable to ones in silicon or gallium nitride.