[musgravepeter]

I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going.

Some books I liked for self study because they have answers:

Introduction to Analysis, Mattock.

Elementary Differential Geometry, Pressley.

There is also recently Needham's Visual Differential Geometry and Forms, which is great.

Edit: I should also mention Topology without Tears (free, online, very good) https://www.topologywithouttears.net/

[vermarish]

I think learning Real Analysis from baby Rudin is like learning Probability Theory from Wikipedia. It's so encyclopedic that if it's your first look at real analysis, it will be too dense to understand, but if it's your second or third look, you will find beauty in its brevity.

[auggierose]

Very pretty book (Needham's), will check it out! I think over 20 years ago I actually attended a house party that Needham was giving in SF. It's a small world.

[susanrigetti]

Agree that Baby Rudin is VERY difficult to study on its own. I recommend only studying it alongside the other two books I listed: Abbott's Understanding Analysis and Spivak's Calculus (which has a solutions manual). Abbott in particular is very straightforward (at least in comparison with baby Rudin haha)

[tzs]

Another point for Abbott is that it was one of the ~400 books Springer made available for free download near the start of the pandemic. I remember there were a few scripts here on HN back then to grab all those books, so many here probably already have a copy.

[voldacar]

Those are good, I also really like Visual Complex Analysis

[threatofrain]

Consider Analysis 1/2 by Terence Tao for introduction to analysis.

[selimthegrim]

Surprised Arnol'd isn't mentioned for ODEs.