Master Mathematics: Suggest Books to Read in Order for Profundity

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Kanol
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Suggest good books to read in an order for one to gain profundity in the particular subject. This may seem to be a rather baffling task, due to the amount of subjects and it's vastness, but if it is done, it could certainly be extremely useful, especially for people like me who are highly intrigued by mathematics and want to learn but find ourselves to be greatly confused on which books to read. This thread can then also serve as the ultimate reference guide but remember, you MUST suggest books in an order to read. For example, on Algebra, you can first suggest books that discuss elementary algebra and then move on to suggesting books that discuss a higher level of algebra.

Algebra

Geometry

Trigonometry

Calculus

Analytic Geometry

Probability & Statistics

Linear Algebra

Abstract Algebra

Ordinary Differential Equations

Partial Differential Equations

Real Analysis

Complex Analysis

Group Theory

Differential Geometry

Lie Groups

Differential Forms

Homology

Cohomology

Homotopy

Fiber Bundles & Characteristic Classes

Index Theorems
 
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