These knots are recommended for joining two ropes of unequal diameters. This type of knot works equally well if the ropes are of the same size too. For more security, you can use a doubled version ...

The Mule Knot (a.k.a releasable knot) is ideal to lock off the rope on the belay plate. There are many occasions in climbing when, belaying from the harness using a device which does not self-arrest ...