Could you give me a list of the most authoritative and prestigious manuals or textbooks for introduction to classic logic currently used in higher education?
Not an exhaustive list, by any means, but here goes:
- David Barker-Plummer, Jon Barwise, John Etchemendy: Language, Proof and Logic
- George Boolos, John Burgess, Richard Jeffrey: Computability and Logic
- Irving Copi, Carl Cohen, Victor Rodych: Introduction to Logic
- Herbert Enderton: A Mathematical Introduction to Logic
- Christopher Leary and Lars Kristiansen: A Friendly Introduction to Mathematical Logic
- Elliot Mendelson: Introduction to Mathematical Logic
- Mark Sainsbury: Logical Forms
- Peter Smith: An Introduction to Formal Logic
- Lori Watson, Patrick Hurley: A Concise Introduction to Logic
Of these, some are aimed more at math students and others more at philosophy students, and perhaps some at both.
I suggest you also peruse Irving M. Copi's Symbolic Logic, which he is supposed to have written as a companion to the Introduction to Logic mentioned by Bumble. (see https://www.journals.uchicago.edu/doi/abs/10.1086/287494.)