The Monster group M is the largest sporadic simple group. It is the group of automorphisms of the 196,884-dimensional Fischer-Griess algebra, which is also a Vertex Operator Algebra (VOA). In 2009, A. A. Ivanov axiomatized several properties of the Fischer-Griess algebra by introducing the notions of Majorana algebra and Majorana representation. Later, Majorana theory was used as a powerful tool to study the structures of the Monster group and Fischer-Griess algebra. Furthermore, in 1971, B. Fischer classified 3-transposition groups with trivial centers and simple derived subgroups. This thesis studies the 3-transposition groups from the Fischer's list, their embeddings into the Monster group, and their standard Majorana representations. Firstly, we find the maximal sizes of symmetric subgroups of Fischer groups generated by their transpositions. Then, we use that information to find which 3-transposition groups from the Fischer's list can be embedded into each other. Finally, we prove that a 3-transposition group from the Fischer's list, except possibly Fi24, admits a standard Majorana representation if and only if it can be embedded into the Monster group as a subgroup generated by 2A involutions.