I’m a bit new to self-studying logic (and rhetoric) but I think you should learn about “Formal fallacies” and “Informal fallacies”. Formal fallacies are those that arguments that are systematically false, like all A is B, some C is A, some C is not B, therefore all C is A. But in real arguments you have to convert those organic arguments into these terms (which could be the hardest part), and then you find out if it is a fallacy… I remember there was a way to find out if arguments are valid based on adding stars, I’ll probably send it later… But be warned, an argument can be “valid”, but still have the wrong premises! You can say, All cats are on fire, therefore some things on fire are cats… and the argument would still be valid, but rest on false premises… Informal fallacies, I think, are somewhat out of the scope of formal logic, but they are still considered faulty arguments, like Strawman…
Mostly Informal fallacies, but I liked that book too!