Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings [0] finally helped me conquer elementary real analysis. It was fast, smooth and streamlined experience. Your millage may vary, though, as this one wasn't my first analysis encounter.

This book enters the pantheon of books that were tremendously helpful to me: Learning to Reason by Nancy Rodgers, Discrete Math by Susanna Epp and Linear Algebra by Kuldeep Singh.

[0] https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-T...

If you have taken some "intro to proofs" or "intro to abstract algebra" or "intro linear algebra" or any other such course where you've seen rigorous proofs, then Jay Cummings' "Real Analysis: A Long-Form Mathematics Textbook" [0] is simply a phenomenal introduction to real analysis. It's a fast paced tour de force through rigorous analysis.

I actually wrote a longer comment, but I had to invoke the names of other authors. Better not. Either way, I love the book.

[0] https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-T...