Active Galactic Nuclei (AGNs) are one of the most luminous persistent sources of
electromagnetic (EM) radiation, with their luminosities much higher than that of a normal
galaxy. One of the defining characteristics of AGNs is their rapid variability from minutes
to year-long timescales in the entire EM spectrum. In the last four decades, AGN
variability has been proven to be one of the most powerful tools to probe the structure
and physics near the central parsec region around supermassive black holes. Albeit,
our understanding of these sources remains contentious due to the statistically limited
or biased samples. Nowadays, with the advent of various new time domain surveys
such as ZTF, it has become possible to study the variability properties of large and
homogeneous samples of AGNs without any observation bias. We have performed an
extensive study of large homogeneous samples in a special subclass of AGNs, known
as blazars, on intra-night to year-long timescales. In this context, we have first studied
the intranight optical variability (INOV) of 92 blazars based on their ZTF light curves and
compared their INOV duty cycle with a 20-fold control sample of radio-quiet quasars
(RQQs). We found the INOV duty cycle of blazars to be much higher than that of RQQs,
and especially for those blazars which have been detected in gamma-rays. Extending
our INOV study to a rare subclass of blazars, TeV blazars, based on 1.3m DFOT
observations, we have tried to understand the origin of the problem of 'Doppler crisis’
based on a well selected sample of 6 TeV blazars for which a lack of superluminal
radio-knots has been established. Following the intranight flux variations in the blazars,
we have tried to search for any possible universality in the long-term color behavior of a
large sample consisting of 897 blazars comprising 455 BL Lacs and 442 Flat Spectrum
Radio Quasars (FSRQs). We found the color behavior of BL Lacs to be dominated by a
Bluer when brighter (BWB) trend, whereas a Redder when Brighter (RWB) trend was
found in most FSRQs, which was however found to further depend on other parameters
like variability amplitude, brightness, etc. Further, we have searched for the periodicities
based on the ZTF light curve in a sample of 2103 blazars and explored the possible
mechanism giving rise to these signatures, detected in 5 such systems in our analysis.
Additionally, we have also worked on the development of a data reduction pipeline for
the 4m International Liquid Mirror Telescope (ILMT), which will be a useful tool for such
systematic photometric variability studies of the AGNs falling on its strip with a 1-day
cadence.