  The Complete Manifold of Ground State Eigenfunctions for the Purely Magnetic
2D Pauli Operator is considered as a by-product of the new reduction found by
the present authors few years ago for the Algebrogeometric Inverse Spectral
Data (i.e. Riemann Surfaces and Divisors). This reduction is associated with
the (2+1) Soliton Hierarhy containing a 2D analog of the famous "Burgers
System". This article contains also exposition of the previous works made since
1980 including the first topological ideas in the space of quasimomenta. We
present here also new results dedicated to the self-adjoint boundary problems
for Pauli Operator. The 2D zero level "nonspectral" Bloch-Floquet functions
give discrete points of additional spectrum similar to the "boundary states" of
finite-gap 1D potentials in the gaps.
