Instiki sports a variety of markup options, but the main one for use with mathematics (that’s why you’re here, after all) is Markdown.
The Markdown implementation is based on Maruku, a greatly enhanced implementation which augments John Gruber’s orginal Markdown syntax with Michel Fortin’s extensions (tables, footnotes, definition-lists, …). It also sports a very nice metadata syntax for adding attributes (id, class, style, etc.) to the generated XHTML.
With the (default) Markdown+itex2MML filter, you can enter equations in itex, a LaTeX-like dialect. Inline and display equations are supported, as is automatic equation numbering and other such niceties.
Internal Wiki links can be generated by
[[Name of Page]]
or
[[Name of Page|Alternate link text]]
You can also link to other Webs on the same Instiki installation, using
[[Name of Web:Name of Page]]
or
[[Name of Web:Name of Page|Alternate link text]]
If you so choose, camel-cased words, like “HomePage” and “IKnowBetter”, can also generate Wiki links (personally, I prefer to disable that in the Edit Web page).
It’s easy to upload files and pictures to your Wiki. To display an uploaded image, called mypic.jpg, you can use
[[mypic.jpg:pic]]
or
[[mypic.jpg|some alt text:pic]]
Similarly, you can link to an uploaded file, myfile.pdf, with
[[myfile.pdf:file]]
or
[[myfile.pdf|some link text:file]]
<nowiki>...</nowiki>
protects its contents from being interpreted. Thus, you can type
<nowiki>[[Not a link]]</nowiki>
and have it appear as [[Not a link]]. At least in this case, the same effect can be achieved using backslashes for escaping, i.e., by typing \[\[Not a link\]\].
You’ve probably noticed the sidebar on the pages of this Wiki. That’s achieved with via a Wiki-include
[[!include Name of Page]]
If, for whatever reason, the extended Markdown syntax, and Wiki syntax, are not rich enough to express what you want, you can always include XHTML in your page. Note that Markdown processing is disabled inside XHTML. Thus
<div>This is **very** bad.</div>
is rendered as
This is **very** bad.
If you want to mix XHTML and Markdown syntax, include the markdown="1" attribute.
<div markdown="1">This is **very** good.</div>
is rendered as
This is very good.