Since the discovery of the first planet outside our Solar System, known as an exoplanet, we have come a long way in their study, from their detection to characterisation. The advent of ultra-precision telescopes such as the CHaracterising ExOPlanet Satellite (CHEOPS), the Transiting Exoplanet Survey Satellite (TESS), and the James Webb Space Telescope (JWST) has enabled us to examine not only the composition of exoplanets, but also their atmospheres. The present thesis introduces the subject of transiting exoplanets and reviews research on close-in exoplanets.

After presenting a brief history of the field and the techniques used to detect exoplanets, we focus on the transit method to characterise exoplanets and their atmospheres. We discuss how a transit (flux drop when a planet passes in front of its host star), occultations (flux change when a planet is blocked by its host star), and phase curves (flux variations throughout planetary orbit) can be used to study planetary bulk, orbital, and atmospheric properties. We then describe how we can exploit the photometric and spectroscopic capabilities of space-based telescopes, together with Bayesian data analysis, to extract the planetary properties from observations. Some of the prime targets to observe in transit geometry are close-in planets. In this thesis, we examine two classes of close-in planets: ultra-short-period rocky planets (USPs) and hot Jupiters. USPs are rocky planets that orbit their host star within about a day. They have very high equilibrium temperatures, resulting in a partially or fully molten surface, which can outgas a thin secondary atmosphere containing rock vapours (e.g., SiO) or volatiles (e.g., CO, CO2). Characterising atmospheres help constrain their atmospheric and interior composition. Hot Jupiters are hot gas giant planets orbiting very close to their host star. They have peculiar atmospheric chemistries with cloudless daysides because of high temperatures, typically resulting in low albedos. Hot Jupiters have a characteristic thermal structure of a strong day-night contrast and a strong eastward jet stream. The hottest among them are known as ultra-hot Jupiters, and they can have a distinct atmospheric structure compared to the cooler hot Jupiters.

Scientific articles presented in this thesis use the transit method to primarily characterise the atmospheres of close-in exoplanets. We use CHEOPS, TESS, and JWST to observe two USPs, TOI-561 b and 55 Cnc e, and two hot Jupiters, WASP-189 b and HD 189733 b, photometrically and/or spectroscopically. Our photometric observations of TOI-561 b not only constrains the internal structure of the planet but also finds a hint of a secondary silicate atmosphere. The spectroscopic observations of 55 Cnc e with JWST reveals a strong variability in the dayside emission, which could be the result of a transient outgassed atmosphere or a circumstellar inhomogeneous dust torus. The photometric observations of hot Jupiters constrains the thermal and reflective properties of those planets. A TESS phase curve of the ultra-hot Jupiter WASP-189 b measures the temperature map of the planet, which helps in estimating Bond albedo and heat redistribution efficiency. Finally, optical observations of cooler hot Jupiter HD 189733 b with CHEOPS uncover a very low geometric albedo. The small albedo is consistent with a cloud-free atmosphere with Rayleigh scattering from hydrogen molecules and sodium absorption.