I don't have a code book but I was wondering do you have to use conduit when wiring a barn or can you use m\c cable?

Yes, either conduit or MC cable, in addition to NM-C cable is allowed.

NM-C cable looks like standard Romex NM-B, but is corrosive resistant, and is allowed in barns, where not subjected to phyical damage.

Any area, such as in range of livestock can damage with kicking hooves, that wiring must be in conduit or something that can resist damage.