So now you're in the file and ready to type beautiful
(and, hopefully, correct) mathematics. One thing always to keep
in mind is that 
commands--i.e., words which when
``ed'' turn into symbols or directions to do things
like underline, center, etc.--are usually preceded with a
backslash,
\ .
Basically, the stuff you type falls into two categories:
math and text.
, correspondingly,
has two ``modes,'' math mode and text mode,
which determine how it responds to the text and commands in
your file. Text mode
is the default. Most commands in text mode change the
appearance and layout of the text on the page (what font it is in, for
instance, and whether it is centered).
In time we'll see examples of most of the useful ones.
Math mode is indicated by a dollar sign:
$ .
Everything between dollar signs is interpreted by as
mathematical symbols and commands.
Enclosing math symbols with single dollar signs gives math within a line of
text. For instance,
...For any such group $G$, let $\rho_i$ be an irreducible representation...gives
...For any such group G, let 
be an irreducible representation...
G put it in
italic, as is usual for math symbols.
The underscore ``_'' generated a subscript. More on that later.
Double dollar signs put the mathematics on its own line and center it:
...Thus, we obtain the following relation: $$\psi = \kappa\cdot \Theta$$ where $\Theta$ is any...produces Thus, we obtain the following relation:
where 
is any...
Most commands work in only one of 's modes.
For instance, the commands which generate math
symbols, like the \rho and \Theta used above,
are only valid in math mode. Similarly, commands to center
text, or to typeset a table or a bibliography,
work only in text mode.
Since the two modes work so differently, we treat text
commands and math commands separately, in
Sections 6 and 7, respectively.