Since the discovery of superconductivity in LaFePO, numerous iron-based superconductors have been identified within diverse structure families. Superconductivity in the layered iron germanide YFe$2$Ge$2$ was first reported in 2014. It stands out from the commonly known iron- based superconductor families for not containing either Group-V or Group-VI elements and has since been predicted to be an unconventional superconductor.

The intermetallic $d$-electron system YFe$2$Ge$2$ exhibits an unusually high Sommerfeld coefficient of $\approx \backslash SI100\backslash milli\backslash joule/\backslash mole\backslash kelvin2$, signalling strong electronic correlations. Its low-temperature normal-state resistivity displays a $T1.5$ power-law temperature dependence, which is an indication of non-Fermi-liquid behaviour. While superconductivity in YFe$2$Ge$2$ has been widely observed below $Tc\approx \backslash SI1.9\backslash kelvin$ in electric transport measurements, evidence of a bulk superconducting transition has proved elusive. This has prompted significant efforts into improving the crystal quality.

In this thesis, I present the crystal growth methods which have successfully produced high-quality poly- and single-crystal YFe$2$Ge$2$ samples. Measurements on these samples have led to conclusive evidence that superconductivity is an intrinsic property of this compound. Disorder effects on both the poly- and single-crystals have been studied through structural investigations, in which anti-site disorder of germanium substitution on the iron site was found to be the dominant factor. The fast suppression of the superconducting transition temperature, $Tc$, of YFe$2$Ge$2$ by disorder suggests an unconventional pairing mechanism. Using a liquid transport flux method, single crystals with residual resistivity ratios ($\mathrm{RRR}=\rho \backslash SI300\backslash kelvin/\rho \backslash SI2\backslash kelvin$) reaching 470 have been synthesised. These crystals exhibit clear bulk superconducting transitions. Low-temperature specific heat and $\mu$SR measurements performed on these crystals provided evidence for multi-gap superconductivity, most likely of the $s\pm$-wave nature, which is compatible with theoretical predictions. Moreover, quantum oscillations have been detected for the first time in dHvA susceptibility and tunnel-diode oscillation measurements of high-quality YFe$2$Ge$2$ single crystals. Although unable to account fully for the high Sommerfeld coefficient, the current results have confirmed significant mass enhancements in the detected Fermi surface sheets.