Reddit reviews Analysis I: Third Edition (Texts and Readings in Mathematics)

Analysis I by Terence Tao.

This is a compilation of what I gathered from reading on the internet about self-learning higher maths, I haven't come close to reading all this books or watching all this lectures, still I hope it helps you.

General Stuff:
The books here deal with large parts of mathematics and are good to guide you through it all, but I recommend supplementing them with other books.

1. Mathematics: A very Short Introduction : A very good book, but also very short book about mathematics by Timothy Gowers, a Field medalist and overall awesome guy, gives you a feelling for what math is all about.
   
   
2. Concepts of Modern Mathematics: A really interesting book by Ian Stewart, it has more topics than the last book, it is also bigger though less formal than Gower's book. A gem.
   
   
3. What is Mathematics?: A classic that has aged well, it's more textbook like compared to the others, which is good because the best way to learn mathematics is by doing it. Read it.
   
   
4. An Infinitely Large Napkin: This is the most modern book in this list, it delves into a huge number of areas in mathematics and I don't think it should be read as a standalone, rather it should guide you through your studies.
   
   
5. The Princeton Companion to Mathematics: A humongous book detailing many areas of mathematics, its history and some interesting essays. Another book that should be read through your life.
   
   
6. Mathematical Discussions: Gowers taking a look at many interesting points along some mathematical fields.
   
   
7. Technion Linear Algebra Course - The first 14 lectures: Gets you wet in a few branches of maths.
   
   Linear Algebra: An extremelly versatile branch of Mathematics that can be applied to almost anything, also the first "real math" class in most universities.
   
   
8. Linear Algebra Done Right: A pretty nice book to learn from, not as computational heavy as other Linear Algebra texts.
   
   
9. Linear Algebra: A book with a rather different approach compared to LADR, if you have time it would be interesting to use both. Also it delves into more topics than LADR.
   
   
10. Calculus Vol II : Apostols' beautiful book, deals with a lot of lin algebra and complements the other 2 books by having many exercises. Also it doubles as a advanced calculus book.
    
    
11. Khan Academy: Has a nice beginning LinAlg course.
    
    
12. Technion Linear Algebra Course: A really good linear algebra course, teaches it in a marvelous mathy way, instead of the engineering-driven things you find online.
    
    
13. 3Blue1Brown's Essence of Linear Algebra: Extra material, useful to get more intuition, beautifully done.
    
    Calculus: The first mathematics course in most Colleges, deals with how functions change and has many applications, besides it's a doorway to Analysis.
    
    
14. Calculus: Tom Apostol's Calculus is a rigor-heavy book with an unorthodox order of topics and many exercises, so it is a baptism by fire. Really worth it if you have the time and energy to finish. It covers single variable and some multi-variable.
    
    
15. Calculus: Spivak's Calculus is also rigor-heavy by Calculus books standards, also worth it.
    
    
16. Calculus Vol II : Apostols' beautiful book, deals with many topics, finishing up the multivariable part, teaching a bunch of linalg and adding probability to the mix in the end.
    
    
17. MIT OCW: Many good lectures, including one course on single variable and another in multivariable calculus.
    
    Real Analysis: More formalized calculus and math in general, one of the building blocks of modern mathematics.
    
    
18. Principle of Mathematical Analysis: Rudin's classic, still used by many. Has pretty much everything you will need to dive in.
    
    
19. Analysis I and Analysis II: Two marvelous books by Terence Tao, more problem-solving oriented.
    
    
20. Harvey Mudd's Analysis lectures: Some of the few lectures on Real Analysis you can find online.
    
    Abstract Algebra: One of the most important, and in my opinion fun, subjects in mathematics. Deals with algebraic structures, which are roughly sets with operations and properties of this operations.
    
    
21. Abstract Algebra: Dummit and Foote's book, recommended by many and used in lots of courses, is pretty much an encyclopedia, containing many facts and theorems about structures.
    
    
22. Harvard's Abstract Algebra Course: A great course on Abstract Algebra that uses D&F as its textbook, really worth your time.
    
    
23. Algebra: Chapter 0: I haven't used this book yet, though from what I gathered it is both a category theory book and an Algebra book, or rather it is a very different way of teaching Algebra. Many say it's worth it, others (half-jokingly I guess?) accuse it of being abstract nonsense. Probably better used after learning from the D&F and Harvard's course.
    
    There are many other beautiful fields in math full of online resources, like Number Theory and Combinatorics, that I would like to put recommendations here, but it is quite late where I live and I learned those in weirder ways (through olympiad classes and problems), so I don't think I can help you with them, still you should do some research on this sub to get good recommendations on this topics and use the General books as guides.

Analysis I and II by Terence Tao https://www.amazon.com/Analysis-Third-Texts-Readings-Mathematics/dp/9380250649

Terry Tao has two books on undergrad analysis. The first volume should be sufficient for your course. A lot of people use Rudin's Principles of Mathematical Analysis as well.