Kripke includes some basic logical notation in his "Identity and Necessity." He always gives an intuitive gloss of what he means, so no background in logic is strictly required to understand what is going on. Still, you may find it helpful to know the following:

A variable by itself in parenthesis (e.g., "(x)") is an instance of the universal quantifier, and may be read as "for all x" or "for every x."

The horseshoe ("") is the conditional, which you may think of as "if...then." So, "p q" may be read as, "If p, then q."

The box ("c") means "necessarily" or "it is necessarily the case that...." So, "c p" may be read as "necessarily p."

The bold dot (".") means logical conjuction, which you may think of as "and." So, "p . q" may be read as "p and q."

So, for example, in light of the above, Kripke's formula (3) (p. 94 in the Stainton collection)

(x)(y) (x=y) [ c (x=x) c (x=y)]

May be read as, "For all x, for all y, if x is equal to y, then if x is necessarily identical to itself, then x is necessarily identical to y"