In this thesis I study the synthesis and basic physical properties characterization on 3$d$, 4$d$ and 5$d$ transition metal compounds. Great success has been obtained in 3$d$ transition metal compounds, in which the electric states are well localized due to the large on-site Coulomb repulsion $U$. Most stoichiometric 3$d$ 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 $\mathrm{Cu_2OSO_4}$, 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 $\mathrm{Cu_2OSO_4}$ 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 $\mathrm{Ca_2RuO_4}$ and $\mathrm{Sr_2RuO_4}$ 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 $\mathrm{MoPO_5}$, and present their magnetic and thermodynamic properties. We found that the $4d^1$ compound $\mathrm{MoPO_5}$ 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-Ir$^{6+}$ iridate $\mathrm{Ba_8Al_2IrO_{14}}$ and a novel layered iridate $\mathrm{Ba_{21}Ir_9O_{43}}$. The synthesis, crystal structure, transport, and magnetic properties of them have been reported. $\mathrm{Ba_8Al_2IrO_{14}}$ is a $p-$type band insulator and shows antiferromagnetic couplings but display no order down to 2 K. $\mathrm{Ba_{21}Ir_9O_{43}}$ 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 $\mathrm{Ir_{0.95}Pt_{0.05}Te_{2}}$ 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.