As I understand it, analysis, algebra and geometry are the three primary subcategories of pure math. What are the “levels” of each of these studies?

For instance, analysis might go:
1. Calculus I, II
2. Vector calculus
3. Real analysis
4. Complex analysis
And each of these levels would have recommended textbooks.
1. Stewart, Apostol Vol I, Spivak
2. Apostol Vol II, Baxandall and Liebeck
3. Rudin I
4. Rudin II, III

How would you fill these out, for algebra and geometry as well as analysis?