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In recent years, electron transport through single molecules has attracted huge attention, since the molecules are promising building blocks for the next generation of electronic devices. To create molecular junctions and probe their electrical properties, intense experimental efforts and theoretical studies are underway. For single molecule electronic applications, an important property is their electrical conductance. In this context, I start my thesis by introducing a general discussion about some basic topics related to single molecule transport theory. Quantum interference effects have recently attracted great interest in studies of the charge transport at the single molecule scale. Within this framework, I study the single molecule conductances of five-membered ring compounds to investigate the effect of molecular symmetry and quantum interference on the charge transport through single molecule junctions. This theoretical and experimental study highlights the presence of destructive quantum interference and more importantly reveals that the control of molecular asymmetry via the heteroatom substitution allows the tuning of destructive quantum interference. Theoretically, I identify similar features over some range of energies using different anchoring groups and elucidate the impact of the anchoring groups on the charge transport through single molecule. Moreover, I find that molecular symmetry has a slight effect on the binding energies of the 1-8 compounds seen in Figure 3.1. Within the phase coherent regime, electron transport through a single molecule junction is described by the transmission coefficient, which describes how electrons pass through a molecule from one electrode to the other. Predicting features related to the transmission coefficient is a powerful tool for probing the electronic structure of molecular systems. In this connection, mid-gap transport theory is considered an efficient and easy method, which utilizes a magic ratio rule (MRR) to predict electrical conductance ratios associated with constructive quantum interference in aromatic molecules. I demonstrate that the MRR can be also applied for antiaromatic molecules and provide a comparison between the transmission coefficients of the aromatic and antiaromatic molecules. Furthermore, I present a theoretical study to investigate the transport properties of C60 using carbon-carbon triple bond anchoring groups and prove the validity of MRR when applied to such non-aromatic molecule.