For nano- and molecular-scale applications, it is crucial to investigate and fully understand the electron transport properties of molecular junctions made up of a scattering region like a molecule coupled to metallic electrodes. The electrical properties of two different kinds of two terminal junctions are presented in the theoretical work contained in this thesis: one deals with gold electrodes, which form gold-molecule-gold structures and the other has single-layer graphene forming a gold-molecule-single-layer-graphene junction. In this thesis, the above investigations into the electrical and thermoelectric properties of molecular junctions utilize the theoretical techniques covered in chapters 2 and 3. Chapter 2 presents an introduction to the density functional theory (DFT). It is followed by an outline of transport theory in Chapter 3, based on Green’s function formalism. Chapter4 represents a study of the electron transport properties of the single-molecule/bilayer molecular junctions, formed from Zinc Tetraphenyl Porphyrin (ZnTPP), small graphene-like molecules (Gr), three derivatives with pyridine backbones, and three alkyl-chain backbones terminated with asymmetric anchor groups: amine (NH2 ), and a direct carbon (CH2 ) bond. Chapter5 studied the same core molecules, junctions with asymmetric electrodes which are gold and a single-layer graphene sheet (SLG).