The essential component of the simulation of quantum systems is the mapping of the fermionic Fock space into qubits and the mapping of the creation and annihilation operators into qubit operators. This work covers the notions of the many-body problem, Slater determinants, second quantization as well as different mapping from the Fock space to the Hilbert space where qubits exist. Finally, this work also contains the development of a Mathematica code that performs two of the mappings mentioned above.