Levelling [1]

The process of making a surface even. This can be achieved by either the Cut and Fill Technique, or Strip and Replace Technique: See Grading.
For small areas of lawn that have a hollow present which needs levelling, then a typical technique which is used is to cut the turf into strips, roll it back, fork over the base, fill the hollow with a suitable topsoil, and refirm the area so as to produce a suitable level for the surface. Finally, the turf is then relaid.
Relevelling a small hollow in a lawn
Cut out area that is to be lifted using an edging iron so that the turf can be relaid later on.
Use a spade, or special turfing iron, to carefully cut the roots to produce a turf of uniform depth. Aim for about 25mm depth of turf; trying to cut it too shallow will often result in the spade cutting back upwards through the surface, making the turf difficult to lift and then relay later on. Gradually roll or peel the turf back until you have exposed the desired are that needs raising up. Once a suitable length of turf has been rolled back then move onto the next one.
Lightly fork and then rake over the surface layer and add in new topsoil to raise up to the desired level. It is important to lightly fork over the existing soil surface so as to produce a ‘key’ into which the new imported soil can be easily mixed by raking. Failing to fork over the underlying soil will often result in layering occurring after the turf has been relaid – this will typically produce shallow rooting, quicker yellower of the turf in dry conditions and less chance of blending back in with the rest of the lawn. If the soil is to be replaced then it would mean digging it out and replacing it, but for most relevelling of small hollows it will just be a matter of adding a small amount of additional topsoil.
Make sure the soil is well trod and rake (typically at least 3 times) to produce a firm base onto which the turf can be relaid. Failure to firm the soil properly will result in it sinkage later on and an uneven lawn surface.
Once the soil has a suitable evenness then it will be time to relay the turf. A light application of a pre-turfing fertiliser (such as Bonemeal) might be considered before relaying the turf.
Once the turf has been relaid there will typically be a small overlap of some of the turf. This is because the previous length of the turf in the slight depression produced a longer length than when it is in a straight line. This small overlap is cut off with the use of an edging iron. Instead of throwing the turf away, or putting it on a compost heap, now might also be a good time to repair any damaged lawn edge if the remaining turf is suitable for such use.
Lay a straight edge, such as a batten of wood, or a long spirit level, over the surface to see how level the finish is. A light topdressing over the turf joins may also be required just to give that final finishing touch and to help the turve edges to blend in more rapidly.