  This paper is devoted to the study of the Cauchy problem of incompressible
magneto-hydrodynamics system in framework of Besov spaces. In the case of
spatial dimension $n\ge 3$ we establish the global well-posedness of the Cauchy
problem of incompressible magneto-hydrodynamics system for small data and the
local one for large data in Besov space $\dot{B}^{\frac np-1}_{p,r}(\mr^n)$,
$1\le p<\infty$ and $1\le r\le\infty$. Meanwhile, we also prove the weak-strong
uniqueness of solutions with data in $\dot{B}^{\frac np-1}_{p,r}(\mr^n)\cap
L^2(\mr^n)$ for $\frac n{2p}+\frac2r>1$. In case of $n=2$, we establish the
global well-posedness of solutions for large initial data in homogeneous Besov
space $\dot{B}^{\frac2p-1}_{p,r}(\mr^2)$ for $2< p<\infty$ and $1\le r<\infty$.
