"An overview of Inter-universal Teichmüller Theory and [...] how we can begin to understand this theory":

http://www.quora.com/Joseph-Heavner/Posts/An-overview-of-Int...

Also, from an anonymous post on 4chan @ http://boards.4chan.org/sci/thread/6931488/are-you-ready-for... :

"How to understand IUTeich from the bottom up:

- Algebra (Israel Gelfand)

- The Method of Coordinates (Israel Gelfand)

- How to Prove It: A Structured Approach (Daniel Velleman)

- Kiselev's Geometry - Planimetry and Stereometry

- Trigonometry (Israel Gelfand)

- What Is Mathematics? An Elementary Approach to Ideas and Methods (Richard Courant)

- A Course of Pure Mathematics (G.H. Hardy)

- Linear Algebra (Kenneth Hoffman and Ray Kunze)

- Elementary Differential Equations (William Boyce and Richard DiPrima)

- Topology (James Munkres)

- Calculus On Manifolds (Michael Spivak)

- Principles of Mathematical Analysis (Walter Rudin)

- Real and Complex Analysis (Walter Rudin)

- Functional Analysis (Walter Rudin)

- Partial Differential Equations (Lawrence Evans)

- Analysis On Manifolds (James Munkres)

- Abstract Algebra (David Dummit and Richard Foote)

- Algebraic Topology (Allen Hatcher)

- Introduction to Smooth Manifolds (John Lee)

- Foundations of Differentiable Manifolds and Lie Groups - (Frank Warner)

- Galois Theory (Harold Edwards)

- Linear Representations of Finite Groups (Jean-Pierre Serre and Leonhard Scott)

- A Classical Introduction to Modern Number Theory (Kenneth Ireland and Michael Rosen)

- Introduction to Analytic Number Theory (Tom Apostol)

- Modular Functions and Dirichlet Series in Number Theory (Tom Apostol)

- Riemannian geometry (Peter Petersen)

- The Theory of the Riemann Zeta-Function (Edward Charles Titchmarsh)

- An Introduction to Teichmüller Spaces (Yoichi Imayoshi and Masahiko Taniguchi)

- A Course in p-adic Analysis (Alain Robert)

- Foundations of p-Adic Teichmuller Theory (Shinichi Mochizuki)

- Mochizuki's papers at http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.htm... "