My Background: Graduate Computer Science student, emphasis in complex programming.
Most programmers never get beyond the first-order (unquantified) predicate calculus introduced in the standard finite math course. This text goes to the next level in formal logic, teaching how to prove or disprove that a quantified expression follows logically from a group of premises.
Copi's notation is concise, leads to elegant proofs, and to proofs which are much shorter than many of the tree methods.
Even if you don't feel that you have the stamina to take on quantified logic, the book is an excellent text to unquantified rules of inference. But the real wealth here is the treatment of UI, UG, EI, and EG. To become fluent with this notation requires diligently working the host of example problems in each chapter, but the result will be problem-solving abilities that are much more flexible than the abilities of mathematics alone. You may find yourself becoming addicted to formal logic! Steve