A metric finished hex nut DIN 934 is designed to go onto a nut or screw with matching threads. This is the most common nut there  is and is available in many thread forms and materials. They are commonly double chamfered (that's the little bevel you see on the outside of the corners, to help avoid sharp edges damaging finished product) and double countersunk (that's the ring you see on the inside above the thread, to help the fastener find its way into the hole). The smallest readily available is 1mm but they certainly are available even smaller. The largest readily available one is m100 in diameter, but larger is available.