Deep galaxy surveys have revealed that the global star formation rate (SFR) density in the universe peaks at 1$\le z \le$2 and sharply declines towards $z = 0$. But a clear picture of the underlying processes, in particular the evolution of cold atomic ($\sim$100 K) and molecular gas phases, that drive such a strong evolution is yet to emerge. MALS is designed to use MeerKAT's L- and UHF-band receivers to carry out the most sensitive (N(HI)$>$10$^{19}$ cm$^{-2}$) dust-unbiased search of intervening HI 21-cm and OH 18-cm absorption lines at $0<z<2$. This will provide reliable measurements of the evolution of cold atomic and molecular gas cross-sections of galaxies, and unravel the processes driving the steep evolution in the SFR density. The large sample of HI and OH absorbers obtained from the survey will (i) lead to tightest constraints on the fundamental constants of physics, and (ii) be ideally suited to probe the evolution of magnetic fields in disks
of galaxies via Zeeman Splitting or Rotation Measure synthesis. The survey will also provide an unbiased census of HI and OH absorbers, i.e. cold gas associated with powerful AGNs ($>$10$^{24}$ W Hz$^{-1}$) at $0<z<2$, and will simultaneously deliver a blind HI and OH emission line survey, and radio continuum survey. Here, we describe the MALS survey design, observing plan and the science issues to be addressed under various science themes.