What are characters/symbols are allowed within CSS class selectors? I know that the following characters are invalid, but what characters are valid?

~ ! @ $ % ^ & * ( ) + = , . / ' ; : " ? > < [ ] \ { } | ` #

You can check directly at the CSS grammar.

Basically¹, a name must begin with an underscore (_), a hyphen (-), or a letter(a–z), followed by any number of hyphens, underscores, letters, or numbers. There is a catch: if the first character is a hyphen, the second character must² be a letter or underscore, and the name must be at least 2 characters long.

-?[_a-zA-Z]+[_a-zA-Z0-9-]*

Identifiers beginning with a hyphen or underscore are typically reserved for browser-specific extensions, as in -moz-opacity.

¹ It's all made a bit more complicated by the inclusion of escaped unicode characters (that no one really uses).

² Note that, according to the grammar I linked, a rule starting with TWO hyphens, e.g. --indent1, is invalid. However, I'm pretty sure I've seen this in practice.