Metal–organic coordination structures are materials comprising reticular metal centers and organic linkers in which the two constituents bind with each other via metal–ligand coordination interaction. 2D metal-organic (or porous coordination) frameworks have attracted tremendous attention in the last two decades owing to their unique electronic, topological, magnetic properties. These properties of 2D metal-organic frameworks suggest many potential applications of the materials, for instance, they might be promising candidates to build functional molecular devices. However, the fabrication of a single layers of 2D metal-organic frameworks remains a great challenge. In this regard, synthesizing conjugated organic monolayer with unique properties is highly desirable. This thesis focuses on the fabrication of 2D metal–organic coordination structures through on-surface synthesis on Au(111), Cu(111) and Ag(111) substrates through on-surface selfassembly. We used scanning tunneling microscopy (STM) as an experimental tool and densityfunctional theory (DFT) as a theoretical tool to characterize the electronic, topological, magnetic properties of the networks at a single-molecular level. This thesis consists of four projects as below: xv In the first project, we synthesize single-layer Ni3(HITP)2 on a Au(111) substrate. We resolve its structure at sub-molecular resolution using STM. The DFT calculations show that upon adsorption on Au(111), the single-layer Ni3(HITP)2 interacts weakly with the substrate and retains its planar structure. Interestingly, the non-trivial topological gap of the free-standing layer is preserved in the surface-adsorbed layer. These results demonstrate that on-surface self-assembly is a viable route to realize 2D-MOFs exhibiting exotic quantum phases. In the second project, we design and synthesize a two-dimensional metal-organic network [Fe3(HITP)2], which comprises a Kagome lattice of Fe atoms. DFT calculation indicates that there is a ferromagnetic ground state and a non-trivial 15 meV gap between the Dirac bands and the flat band. Experimentally, we synthesize this structure on a Au(111) surface. We study this structure at a single-molecule resolution and confirm that the on-surface structure is nearly identical to the free-standing framework. We also use scanning tunneling spectroscopy (STS) to reveal the presence of a magnetic moment on Fe atoms in the framework. In the third project, we study the coordination behavior of Ni, Pt, Pd metal with 2,3,6,7,10,11- Hexaaminotriphenylene (HATP) molecules on a Ag(111) surface. We confirm that the coordination reaction can happen with all three metals and also resolve the metal-organic coordination structures at an atomic resolution. In the last project, we synthesize single-layer 2D-MOF structures of Ni3(HAT)2 and Fe3(HAT)2 networks on a Ag(111) surface, and Cu3(HAT)2 networks on a Cu(111) surface. The high resolution STM images show that the Ni3(HAT)2 and Fe3(HAT)2 networks are not flat but titled out of plane on the Ag(111) surface, while the Cu3(HAT)2 network can grow into larger and flat networks on the Cu(111) surface. Moreover, we use STS to study the coordinated Fe in Fe3(HAT)2 coordination network. The double-step structure in the STS spectra indicates that the coordinated Fe atoms undergo spin-flip processs. In summary, we design and synthesize many 2D metal-organic frameworks which comprises a Kagome lattice of coordinated metal atoms. These studies may contribute to the development of low-dimensional conjugated metal-organic materials.