The Galileo has several options for Serial interfacing, including UART, I2C and SPI
In order to connect to the M-BUS you would need an m-bus interface shield.
As far as I know the M-BUS system works on a 2-wire system for communicating with energy meters.
Since it uses custom driver chips and not standard RS232 you'd need to build or obtain an M-BUS shield.
Most M-BUS systems use the TSS721A chip, which has a TX/RX interface to the host (galileo) which could be connected to pins 0 and 1 of the shield.
The protocol would need to be decoded, and you'd need to be aware that you might be interfacing LIVE mains with high current capacities, which may not be compatible with continued existence, either of the Galileo or any person near it.
You'd need some code to decode the M-BUS protocol, but it is well documented.