Compressible turbulence plays a critical role in a wide range of applications, from the mixing processes in scramjet engines to astrophysical phenomena. While velocity measurements have provided valuable insights into turbulent flows, thermodynamic variables such as density and temperature are equally important for understanding the effect of compressibility on turbulence dynamics. Previous research has shown that density statistics reveal compressibility at lower Mach numbers compared to velocity statistics. Theory shows that density structures contain slower, larger motions than velocity structures. While many simulations have analyzed density fluctuations, there is a scarcity of experimental data in this area. Measuring density in turbulent flows presents experimental challenges in capturing non-intrusive, high-frequency data due to the high speeds involved and complicated, sensitive setups required. Density gradients are much more accessible through optical methods while also providing insights into the dynamics of turbulent behavior. In this dissertation, we present a detailed experimental investigation of density gradient statistics in a compressible turbulent jet using time-resolved schlieren imaging. In the first part of this work, we develop and validate a quantitative schlieren technique for measuring density gradients in the Variable Density and Speed of Sound Vessel (VDSSV). By carefully calibrating the optical system, we extract gradient information from schlieren images with sufficient fidelity to resolve inertial-range statistics. Through experiments in both air and sulfur hexafluoride (SF6), we isolate the influence of the Mach number on density gradient fluctuations while maintaining comparable Reynolds numbers. We find that the schlieren system accurately measures density gradients in the facility with sufficient sensitivity to resolve turbulent fluctuations at inertial scales. In the second part of this work, we analyze the statistical properties of density gradients at inertial scales. Temporal correlation functions exhibit the expected decorrelation, with minima that increase monotonically with Mach number, suggesting enhanced intermittency. Zero-crossing time scales decrease with increasing Mach number, consistent with faster convection. However, the corresponding spatial length scales show an opposing trend, bringing the validity of Taylor's hypothesis into question for these measurements. Probability density functions exhibit near-Gaussian behavior, with longitudinal density gradients showing increasingly positive skewness relative to transverse gradients as Mach number increases, indicating that compressibility occurs predominantly in the streamwise direction. We observe that the variance of density gradients increases with the fourth power of the Mach number, in agreement with previous experiments and simulations at low Mach numbers, and also with the fourth power of the Reynolds number. Through variance ratios, our measurements reveal that when isolating the effect of the Mach number from the Reynolds number, the variance increases instead with approximately the square of the Mach number, a signature of compressible behavior. In the final part of this work, we examine the density gradient spectra. We identify a potential inertial subrange where we find a modest trend toward shallower slopes with increasing Mach number that is consistent with DNS predictions, but not yet statistically conclusive. Through an anisotropy ratio, we observe that the structures do not exhibit a preferential direction. At matched Reynolds number, the ratio of spectra in air to SF6 decays following a slope near -1/4 for all Mach numbers in the identified inertial subrange, demonstrating a consistent scaling relationship across flow conditions. The observed sensitivity of density gradient statistics to weak compressibility effects suggests their potential as diagnostic tools for identifying acoustic phenomena, extreme events, and other compressible structures in practical flows.