TITLE: Computing the Hilbert class field
QUESTION [11 upvotes]: Does anyone know any good source with nice examples of Hilbert class field computations? I'm trying to piece together the theory with some canonical examples.

REPLY [13 votes]: You will find a lot of material on quadratic, cubic and quartic unramified extensions of quadratic number fields in the Seminar on complex multiplication (Borel, Chowla, Herz, Iwasawa, Serre) published in Springer's Lecture Notes 21. Beware of typos, however.
The primary source for unramified cyclic extensions of number fields is the thesis by 
G. Gras, parts of which were published in Extensions abéliennes non ramifiées de degré premier d'un corps quadratique,
Bull. Soc. Math. Fr. 100 (1972), 177-193; there are, however, no exercises there.