Time-domain astronomy studies astronomical sources that change over timescales ranging from minutes to years. These include transient events such as supernovae (SNe) and galactic novae, as well as variable sources such as active galactic nuclei (AGNs) and variable stars. The rapid growth of time-domain surveys has made automated data processing essential for transient detection, particularly because difference image analysis (DIA) can produce large numbers of spurious detections along with genuine astrophysical transients and variables. The 4-m International Liquid Mirror Telescope (ILMT), located at the Devasthal Observatory in India, provides a unique platform for such studies by repeatedly surveying a 22.3-arcmin-wide strip of the zenith sky in the SDSS g′, r′, and i′ bands. This thesis presents the development and scientific application of PyLMT, an end-to-end pipeline designed to automate the detection and classification of transient and variable source candidates in ILMT observations. The pipeline combines image subtraction with automated candidate detection using a convolutional neural network (CNN)-based real/bogus classifier to identify genuine astrophysical sources, followed by a CNN-based classification of detected candidates based on host context. Cross-matching with astronomical catalogues provides additional information for candidate vetting and characterisation. A major challenge in developing these machine-learning models was the limited availability of a labelled ILMT training dataset. This was addressed using transfer learning, data augmentation, and stellar sources as proxies for genuine astrophysical detections. PyLMT has been operational since November 2023 and has so far processed approximately 3700 full-frame ILMT images, producing around 23,000 near-real-time alerts corresponding to transient and variable sources. The resulting sample includes approximately 500 variable stars, including 13 previously uncatalogued variables that were subsequently characterised into subtypes, including eclipsing binaries and BY Draconis variables. It also includes 130 variable AGNs, 21 SN candidates with five new discoveries, and an ambiguous transient candidate. The associated data have been made publicly accessible through the custom-developed DART dashboard. Overall, this work demonstrates that meaningful time-domain science can be done with specialised telescopes having relatively small fields of view and limited labelled datasets, and provides a practical framework for developing automated transient surveys under such constraints.