  We propose an approach to treat (1+1)--dimensional fermionic systems based on
the idea of algebraic bosonization. This amounts to decompose the elementary
low-lying excitations around the Fermi surface in terms of basic building
blocks which carry a representation of the W_{1+\infty} \times {\overline
W_{1+\infty}} algebra, which is the dynamical symmetry of the Fermi quantum
incompressible fluid. This symmetry simply expresses the local particle-number
current conservation at the Fermi surface. The general approach is illustrated
in detail in two examples: the Heisenberg and Calogero-Sutherland models, which
allow for a comparison with the exact Bethe Ansatz solution.
