In this thesis I study the synthesis and basic physical properties characterization on 3d, 4d and 5d transition metal compounds. Great success has been obtained in 3d transition metal compounds, in which the electric states are well localized due to the large on-site Coulomb repulsion U. Most stoichiometric 3d transition metal oxides are antiferromagnetic Mott insulators. Among them, low dimensional geometrically frustrated systems, such as S = 1/2 Kagome lattice antiferromagnets, are at the forefront of condensed matter research. Recently, high-quality single crystals of Cu2OSO4, which are spin-1/2 antiferromagnets with low dimensional magnetism, have been successfully synthesized. The measurements of specific heat, susceptibility and magnetization were performed on this material. We found that the Kagome-like compound Cu2OSO4 shows typical signatures for a canted-AFM ground state with a weak ferromagnetic component. On the other hand, 4d transition metal compounds were considered as weakly correlated systems because the electron correlation is expected to be weaker in 4d transition metal compounds compared with the 3d ones. The 4d ones naturally bridge two different regimes of the strongly correlated 3d compounds and the 5d compounds. Most notably, for instance, it is intriguing that seemingly similar Ca2RuO4 and Sr2RuO4 display totally different behavior: the former is a Mott insulator while the latter is metallic and becomes superconducting at low temperature. Here we report the synthesis of large single crystals of MoPO5, and present their magnetic and thermodynamic properties. We found that the 4d1 compound MoPO5 is orbitally quenched and orders into an antiferromagnet with the moments along c axis. Spin-flop transition is observed which indicates magnetic anisotropy. 5d orbitals are more extended and the Coulomb repulsion U values are expected to be further reduced compared with those of 3d and 4d transition metal compounds. Thus, insulating behaviors in 5d transition metal compounds have been puzzling. A possible reason is the strong spin-orbit coupling. Here we show the ambient-pressure synthesis and physical properties of a new all-Ir6+ iridate Ba8Al2IrO14 and a novel layered iridate Ba21Ir9O43. The synthesis, crystal structure, transport, and magnetic properties of them have been reported. Ba8Al2IrO14 is a p−type band insulator and shows antiferromagnetic couplings but display no order down to 2 K. Ba21Ir9O43 is an insulator with antiferromagnetic Curie-Weiss behavior, where a magnetic transition is suppressed down to low temperature of 9 K despite the large Curie-Weiss temperature of −90 K. We also performed the pressure-dependent resistivity measurements of the 5d compound Ir0.95Pt0.05Te2 and found that the charge order with q=(1/5,0,1/5) dimer configuration is introduced and the superconductivity undergoes a dimensionality cross-over from 3 dimension to 2 dimension under pressure