Quasar microlensing is a relatively newly explored phenomenon, which is ideally suited for studying the spatial distribution of emission from the innermost accretion disc. By now we know many macrolensed quasars, in which we can observe multiple images formed by the deflection of light in the gravitational field of an intervening galaxy. In case one of these images passes directly through the stellar population of the galaxy, it can be additionally microlensed by individual stars. The gravitational field of these stars forms a caustic network for light passing by. When a quasar accretion disc crosses behind this network, induced changes can be observed in the light curve as well as in the spectrum. In the first part of this thesis we study the statistics of the time intervals between successive caustic crossings. In the second part we use a fully relativistic Kerr-metric thin-disc model for studying the light curve of a fold-caustic crossing and its dependence on the accretion- disc parameters. In the last part we simulate changes in the X-ray iron-line profile during a fold-caustic crossing. We find characteristic spectral features formed on the line, and derive their analytical description. Finally, we map the maximum strength of microlensing-generated peaks on the spectral line for different...

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Study of the time variable sources and phenomena in Astrophysics provides us with important insights into the stellar evolution, galactic evolution, stellar population studies and cosmological studies such as number density of dark massive objects. Study of these sources and phenomena forms the basis of Time Domain surveys, where the telescopes while scanning the sky regularly for a period of time provides us with positional and temporal data of various Astrophysical sources and phenomena happening in the Universe. Our vantage point within the Milky Way galaxy greatly limits studying our galaxy in its entirety. In such a scenario our nearest neighbour The Andromeda galaxy (M31) proves to be an excellent choice as its proximity and inclination allows us to resolve millions of stars using space based telescopes. Zwicky Transient Facility (ZTF) is a new optical time domain survey at Palomar Observatory, which has collected data in the direction of M31 for over 6 months using multiple filters. This Thesis involves exploitation of this rich data set. Stars in M31 are not resolved in ZTF as it is a ground based facility. This requires us to use the large public catalogue of stars observed with Hubble Space Telescope (HST): The Panchromatic Hubble Andromeda Treasury (PHAT). The PHAT catalogue provides us with stellar coordinates and observed brightness for millions of resolved stars in the direction of the M31 in multiple filters. Processing of the large volumes of data generated by the time domain surveys, requires us to develop new data processing pipelines and utilize statistical techniques for determining various statistical features of the data and using machine learning algorithms to classify the data into different categories. End result of such processing of the data is the astronomical catalogues of various astrophysical sources and phenomena and their light curves. In this thesis we have developed a data processing and analysis pipeline based on Forced Aperture Photometry Technique. Since the stars are not resolved in ZTF, we performed photometry at pixel level. Only small portion of the ZTF dataset has been analyzed and photometric light curves have been generated for few interesting sources. In our preliminary investigations we have used a Machine Learning Algorithm to classify the resulting time series data into different categories. We also performed cross comparison with data from other studies in the region of the Andromeda galaxy.