  We extend Gesztesy-Holden's method to 2+1 dimensional case to obtain a
unified construction to the algebro-geometric solutions of the whole modified
Kadomtsev-Petviashvili (mKP) hierarchy. Our tools include the relations between
solutions of the Gerdjikov-Ivanov (GI) and mKP hierarchy, the Baker-Akhiezer
functions in 2+1 dimensions, a special function $\psi_1(P)\psi_2(P^*)$ on
$X\times \mathbb{R}^3$ and Dubrovin-type equations for auxiliary divisors.
