  We present a multi-wavelength study of the active nucleus and the off-nuclear
X-ray sources in the nearby spiral galaxy, NGC 1365 using three simultaneous
UV/X-ray observations by AstroSat over a two months period and archival IR
observations performed with Spitzer and Herschel. Utilising the data from the
Soft X-ray Telescope (SXT) on-board AstroSat, we find spectral variability
mainly caused by the variation in the X-ray column density, (N$_H$ $\sim$
10$^{22}$ - 10$^{23}$ cm$^{-2}$). With the accurate spatial resolution of the
UVIT onboard AstroSat, we separate the intrinsic AGN flux from the host galaxy
emission and then correct for the Galactic and the internal reddening. We
detect no significant variation in the NUV emission over the observation
period. The AGN in FUV band is undetectable due to heavy intrinsic extinction.
Further, the multi-wavelength IR/UV/X-ray AGN SED reveals that the AGN is in a
low luminosity phase with accretion rate $\sim$ 0.01 L$_{Edd}$. The steady UV
emission and strong X-ray absorption variability suggest that the obscuring
clouds are likely compact and affect the compact X-ray source only and do not
possibly cover the extended UV emitting region. In addition, the UVIT is able
to resolve two bright spots at a radius of 7" ($\sim$ 6.3 Kpc) from the central
nucleus in the South-West (SW) direction. In the UVIT image of the entire
galaxy, we identify UV counterparts to four Chandra identified bright X-ray
sources. One well-known ultra-luminous X-ray source (ULX) NGC 1365 X2 is
identified with its UV counterpart at 86" from the nucleus in the north-east
(NE) direction from the active nucleus.
