Here is a free text book that covers most of the notation, except the quantifiers, around page 30 or so:

https://www.textbookequity.org/Textbooks/Magnus_forallx.pdf

For the quantifiers, check out the Wikipedia page here:

https://en.m.wikipedia.org/wiki/Quantifier_(logic)

For deeper coverage, the section on first order logic here is quite good:

https://www.amazon.com/Introduction-Montague-Semantics-Synth...