The word Monster refers to the group of that name. Ronan goes into Borcherds' proof of the Conway-Norton conjecture. Here is a nice 2 page article by Borcherds himself. It involves the j invariant, which came up in this recent PF thread. Physicists are interested in the Monster because of its connection with bosonic String theory. See for example the work of Tuite on genus 2 CFT.
Ronan doesn't go into that much mathematics, but he does mention some really wonderful stuff, like the Leech lattice, or the fact that the sum of the first 24 squares is the same as 70 squared!