This is a brief introduction to Fredholm theory for Hilbert space operators
organized into ten sections. The classical partition of the spectrum into
point, residual, and continuous spectra is reviewed in Section 1. Fredholm
operators are introduced in Section 2, and Fredholm index in Section 3.
The essential spectrum is considered in Section 4, the spectral picture is
presented in Section 5, and Riesz points are discussed in Section 6. Weyl
spectrum is the subject of Section 7 and, after bringing some basic results
on ascent and descent in Section 8, Browder spectrum is investigated in
Section 9. Finally, Weyl and Browder theorems close this expository paper
in Section 10.