What is Reddit's opinion of Mathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics)?

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Are you looking for something like Mathematical Logic by Ebbinghaus, Flum, and Thomas? It's not as broad and comprehensive as the book by Curry, and of course Curry is one of the great names in the field. But it is one of the standard modern textbooks.

That’s not a great book for learning logic. I’m honestly not sure where to tell you to start with sequent calculus. I know that Ebbinghaus, Flum, and Thomas cover sequent calculus from a very rigorous mathematical perspective. You can also find some good material in the Open Logic Project textbook. One other option that is maybe a little too daunting for a complete beginner is Troelstra and Schwichtenberg ‘basic proof theory’.