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The Large Array Survey Telescope (LAST) is designed to survey the variable and transient sky at high temporal cadence. The array is comprised of 48 F/2.2 telescopes of 27.9cm aperture, coupled to full-frame backside-illuminated cooled CMOS detectors with $3.76$$\mu$m pixels, resulting in a pixel scale of $1.25\mathrm{arcsec}$. A single telescope with a field of view of $7.4\mathrm{deg}^2$ reaches a $5\sigma$ limiting magnitude of $19.6$ in $20$s. LAST 48 telescopes are mounted on 12 independent mounts -- a modular design which allows us to conduct optimized parallel surveys. Here we provide a detailed overview of the LAST survey strategy and its key scientific goals. These include the search for gravitational-wave (GW) electromagnetic counterparts with a system that can cover the uncertainty regions of the next-generation GW detectors in a single exposure, the study of planetary systems around white dwarfs, and the search for near-Earth objects. LAST is currently being commissioned, with full scientific operations expected in mid 2023. This paper is accompanied by two complementary publications in this issue, giving an overview of the system (Ofek et al. 2023a) and of the dedicated data reduction pipeline (Ofek et al. 2023b).