I have a copy and like it much. However, i was always partial to Frege's Begriffschrift. His notation was really creative. It's a shame Russel's deflation of that project has sentenced it to the rubbish heap of history.
You are confusing his book Begriffsschrift ("concept notation"), where he invented what became modern predicate logic, and his later work "Grundgesetze der Arithmetik" (I/II) which (unsuccessfully) tried to derive arithmetic from purely logical notions, and which made heavy use of the Begriffsschrift.
> he announced the discovery to Gottlob Frege of the paradox in Frege's 1879 Begriffsschrift