The close proximity of the Local Group galaxy M31 provides us with the
opportunity to study its surrounding circumgalactic medium and the
intergalactic medium in detail. I will present my research on mapping and
analysing the diffuse neutral hydrogen gas (HI) that exists within Local
Group. I will discuss the discovery and possible origins of HI clouds that
lie between the galaxies M31 and M33 as well as the faint HI now confirmed
to the northwest of M31. I will also briefly summarize our ongoing and
planned future work.