Quote by Math Is Hard
Hi Tom,
My goodness! I don't think I have ever seen anything like that.

Yes, the Stanford Encyclopedia is really great. When I found it, I tracked down all the articles dealing with logic, printed them out, and put them in binders. It's like getting a few free textbooks.
Modal logic looks very complex, but interesting. I am just now finishing my very first course in logic. I have seen the arrow symbol, as in P > Q, but that's about the only notation that looked familiar.

The other logical symbols are defined at the beginning. Basically, it is regular propositional/quantificational logic, with two new operators:
It is necessary that (denoted by a box)
It is possible that (denoted by a lozenge)
The operators obey rules that look formally similar to the universal and existential quantifiers. If I knew how to TeX, I'd post those rules here. Later I'll dig through that document and find them.
It says that "an understanding of modal logic is particularly valuable in the formal analysis of philosophical argument". What sort of questions do you tackle with modal logic?

Questions of necessity and of possibility.
In addition, some accounts of modal logic include all of the operators listed at the beginning of the document. You probably noticed when taking your course in logic that translating statements from English to logic sometimes resulted in a loss of meaning. For instance, you would translate the statement "Radiation causes cancer" as "If you are irradiated, then you will get cancer", or "r>c". But the conditional has nothing to do with causality, so that shade of meaning is lost when translating into propositional logic. Modal logic is the result of an effort to allow for greater depth of expression in formal statements.
More later, must get back to work...