Over 5000 exoplanets have been discovered in the last three decades, revealing a truly diverse population of worlds beyond our solar system. The field has accelerated rapidly towards characterising the atmospheres of exoplanets around the nearest and brightest stars with large observational surveys from ground-based and space-based instruments. This thesis contains an overview of state-of-the-art methods for detecting chemical species in the atmospheres of transiting exoplanets. In the first chapter, I briefly review the history, key insights, and modern techniques for detecting exoplanets and studying their atmospheres. The subsequent chapters are each based on specific aspects of the analysis of high-resolution transmission spectra in optical wavelengths, aimed towards answering key questions regarding detrending techniques and the atmospheric properties of highly irradiated giant exoplanets.

I begin by assessing the robustness of telluric correction methods for removing contaminating telluric water and oxygen lines from high-resolution spectra. This is a challenging and critical task when observing from the ground since absorption from Earth’s atmosphere often overwhelms the exoplanetary signals by several orders of magnitude. I compare the performance of corrections made using a telluric spectrum derived empirically from airmass and using a model of Earth’s transmission spectrum, focusing specifically on sodium detections in the transmission spectrum of a hot Jupiter.

Next, I explore the diversity of ten highly irradiated giant exoplanets with equilibrium temperatures ranging from around 1000 to 4000 K. I conduct a homogeneous survey of sodium absorption using high-resolution transmission spectra extracted from observations made with the HARPS and HARPS-N spectrographs. Using sodium as a tracer, I report uniformly measured atmospheric properties across the sample, including atmospheric heights, net day-night wind speeds, and sodium doublet line ratios. I report a new detection of sodium in one of the planets and confirm previously reported detections in the others. I also discuss how different assumptions and detrending processes can cause discrepancies in the measured absorption features, highlighting the importance of a homogeneous analysis when comparing results across multiple planets.

I then use these results to perform a search for new global trends on planetary atmospheric properties, with the goal of understanding how the characteristics of the atmospheres change over a diverse sample of planets. I investigate how the homogeneously measured atmospheric heights (as probed by detections of sodium) vary with macroscopic planetary properties, revealing an empirical relationship describing the relative atmospheric heights as a function of planetary equilibrium temperature and surface gravity. I also use the sodium detections to measure net atmospheric wind velocities for all ten planets and discuss how these results can provide information about common underlying processes and dynamics.

Finally, I investigate signatures of other atomic species in optical high-resolution transmission spectra of two ultra-hot Jupiters using the cross-correlation technique. In particular, I search for prominent metallic species that are expected to be present due to the extreme temperatures of these exotic atmospheres. I compare the atmospheric heights derived from high-significance detections of neutral iron between the two targets. I also discuss tentative inferences of asymmetric iron absorption features, where the signals from the atmosphere become progressively more blueshifted in the first half of the transit up to a constant value. This asymmetry is indicative of different atmospheric structure or chemistry between the morning and evening terminators.

I conclude with final remarks on promising avenues for future research over the course of the next decade, where high-resolution spectroscopy will play a pivotal role in furthering our understanding about the atmospheric properties and processes of the diverse population of exoplanets.