<p>Experiments at Jefferson Lab have been conducted to extract the nucleon spin-dependent structure functions over a wide kinematic range. Higher moments of these quantities provide tests of QCD sum rules and predictions of chiral perturbation theory ($\chi$PT). While precise measurements of $g_{1}^n$, $g_{2}^n$, and $g_1^p$ have been extensively performed, the data of $g_2^p$ remain scarce. Discrepancies were found between existing data related to $g_2$ and theoretical predictions. Results on the proton at large $Q^2$ show a significant deviation from the Burkhardt-Cottingham sum rule, while results for the neutron generally follow this sum rule. The next-to-leading order $\chi$PT calculations exhibit discrepancy with data on the longitudinal-transverse polarizability $\delta_{LT}^n$. Further measurements of the proton spin structure function $g_2^p$ are desired to understand these discrepancies.</p><p>Experiment E08-027 (g2p) was conducted at Jefferson Lab in experimental Hall A in 2012. Inclusive measurements were performed with polarized electron beam and a polarized ammonia target to obtain the proton spin-dependent structure function $g_2^p$ at low Q$^2$ region (0.02$<$Q$^2$$<$0.2 GeV$^2$) for the first time. The results can be used to test the Burkhardt-Cottingham sum rule, and also allow us to extract the longitudinal-transverse spin polarizability of the proton, which will provide a benchmark test of $\chi$PT calculations. This thesis will present and discuss the very preliminary results of the transverse asymmetry and the spin-dependent structure functions $g_1^p$ and $g_2^p$ from the data analysis of the g2p experiment .</p> / Dissertation