  The magnetoresistance is the magnetic field induced change of electrical
resistivity of a material. Recent studies have revealed extremely large
magnetoresistance in several non-magnetic semimetals, which has been explained
on the basis of either electron-hole compensation or the Fermi surface
topology, or the combination of both. Here, we present a single crystal study
on MoSi$_2$, which exhibits extremely large magnetoresistance, approaching
almost 10$^7$ % at 2 K and 14 T magnetic field. It is found that the
electron-hole compensation level in MoSi$_2$ evolves with magnetic field, which
is resulted from strong Zeeman effect, and found beneficial in boosting the
large non-saturating magnetoresistance. The non-trivial Berry phase in the de
Haas-van Alphen oscillations and the moderate suppression of backward
scattering of the charge carriers lend support for the topological nature of
this semimetal. The ultra-large carrier mobility of the topologically protected
charge carriers reinforces the magnetoresistance of MoSi2 to an unprecedented
large value.
