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In the first half of this seminar we will make an introduction to "Moonshine". Namely, we will talk about modular forms, Hecke operators, the Monster Group, Kac-Moody-Lie algebras, vertex algebras, replicability of power series and how these structures are all interrelated to each other. We will introduce the McKay-Thompson series $T_g$, which are modular functions associated to each element $g$ in the Monster group. An interesting fact is that all Mckay-Thompson series are replicable and replication respects the power map structure in the Monster in the sense that $T_g^{(n)}=T_{g^n}$, where $T_g^{(n)}$ is the $n$-th replicate of $T_g$. Even though replicability can be defined in an very elementary way, the real motivation comes from the Hecke operators for the modular group. We make this observation the starting point of the second part of the seminar where we will find the Hecke operators for the group $\Gamma_0(2)+$. From this, we obtain a new definition of replicability that we call 2A-replicability. It turns out that it reflects (as replicability does for the Monster) the power map structure in the Baby Monster group, which arises as a centralizer of an element of class 2A in the Monster, whence the notation.
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