While the presence of gaseous enclosures observed at various solid-water interfaces, the so-called "surface nanobubles", has been confirmed by many groups in recent years, their formation, properties, and stability have not been convincingly and exhaustively explained. Here we report on an atomic force microscopy (AFM) study of argon nanobubbles on highly oriented pyrolitic graphite (HOPG) in water to elucidate the properties of nanobubble surfaces and the mechanism of AFM tip-nanobubble interaction. In particular, the deformation of the nanobubble-water interface by the AFM tip and the question whether the AFM tip penetrates the nanobubble during scanning were addressed by this combined intermittent contact (tapping) mode and force volume AFM study. We found that the stiffness of nanobubbles was smaller than the cantilever spring constant and comparable with the surface tension of water. The interaction with the AFM tip resulted in severe quasi-linear deformation of the bubbles; however, in the case of tip-bubble attraction, the interface deformed toward the tip. We tested two models of tip-bubble interaction, namely, the capillary force and the dynamic interaction model, and found, depending on the tip properties, good agreement with experimental data. The results showed that the tip-bubble interaction strength and the magnitude of the bubble deformation depend strongly on tip and bubble geometry and on tip and substrate material, and are very sensitive to the presence of contaminations that alter the interfacial tension. In particular, nanobubbles interacted differently with hydrophilic and hydrophobic AFM tips, which resulted in qualitatively and quantitatively different force curves measured on the bubbles in the experiments. To minimize bubble deformation and obtain reliable AFM results, nanobubbles must be measured with a sharp hydrophilic tip and with a cantilever having a very low spring constant in a contamination-free system.