Space is not a void but a mosaic of tiny cells. In loop quantum gravity, spacetime curvature is transferred from a smooth sheet to a network of 'atoms' of volume — spin networks. Each node of such a network is a quantum of space, and the links between them are quanta of area.
But how does this mosaic change over time? That's where spin foams come in. This is not a frozen picture but a history of transitions: the network pulses, rearranges, and gives birth to new cells. The lecture authors take the listener from simple to complex: first a two-dimensional world where gravity is almost toy-like, then a three-dimensional one — with the Ponzano–Regge model (a quantum analogue of a geodesic dome), and finally the four-dimensional one we live in. Each step is a sum over all possible 'foamy' histories, and from the sum emerges familiar gravity.
This view turns general relativity into an almost topological theory: the coarse features of space (number of holes, connectivity) matter more than fine details. It's like knitting: the pattern (topology) is set, and the needles (quantum fluctuations) only add loops. The lectures are a brief guide to this construction of reality, from a flat world to our voluminous one.
In three-dimensional quantum gravity, there are no gravitons — the particles that carry gravity. There, geometry is 'frozen' and cannot fluctuate as it does in our world.