Don't know if anyone has suggested it here (I'd honestly be surprised if someone hasn't) but Principles of Mathematical Analysis by Walter Rudin, affectionatey known as "Baby Rudin" is a classic book. It's known for being relatively difficult and dense if you're just beginning with analysis, but if you go through the book and complete a fair number of exercises, it's an incredibly rewarding experience and definitely grants a ton of mathematical maturity.
