Better script fonts for maths

The font selected by \mathcal is the only script font ‘built in’. However, there are other useful calligraphic fonts included with modern TeX distributions.

The eucal package (part of most sensible TeX distributions; the fonts are part of the AMS font set) gives a slightly curlier font than the default. The package changes the font that is selected by \mathcal.

Type 1 versions of the fonts are available in the AMS fonts distribution.

The mathabx bundle provides calligraphic letters (in both upper and lower case); the fonts were developed in MetaFont, but a version in Adobe Type 1 format is available. The bundle’s documentation offers a series of comparisons of its calligraphic set with Computer Modern’s (both regular mathematical and calligraphic letters); the difference are not large.
The mnsymbol bundle provides (among many other symbols) a set of calligraphic letters, though (again) they’re rather similar to the default Computer Modern set.
The mathrsfs package uses a really fancy script font (the name stands for “Ralph Smith’s Formal Script”) which is already part of most modern TeX distributions (Type 1 versions of the font are also provided, courtesy of Taco Hoekwater). The package creates a new command \mathscr.
The bundle rsfso provides a less dramatically oblique version of the RSFS fonts; the result proves quite pleasing — similar to the effect of the the (commercial) script font in the Adobe Mathematical Pi collection.
Zapf Chancery
is the standard PostScript calligraphic font. There is no package but you can easily make it available by means of the command
in your preamble. You may find the font rather too big; if so, you can use a scaled version of it like this:
\DeclareFontShape{OT1}{pzc}{m}{it}{<-> s * [0.900] pzcmi7t}{}
Adobe Zapf Chancery (which the above examples use) is distributed in any but the most basic PostScript printers. A substantially identical font (to the extent that the same metrics may be used) is available from URW, called URW Chancery L: it is distributed as part of the “URW base35” bundle; the urwchancal package (which includes virtual fonts to tweak appearance) provides for its use as a calligraphic font.

The TeX Gyre font family also includes a Chancery replacement, Chorus; use it with tgchorus (and ignore the complaints about needing to change font shape).

Examples of the available styles are linked from the packages’ catalogue entries.
Distributed as part of amsfonts
euler fonts
Distributed as part of amsfonts
mathabx as MetaFont
mathabx in Type 1 format
Distributed as part of jknappen-macros
mnsymbol fonts
rsfs fonts
rsfso fonts
Script font examples
TeX Gyre Chorus font family
Distributed as part of tex-gyre
URW Chancery L
Distributed as part of urw-base35

This answer last edited: 2011-08-17