(High-Dimensional) Convex Geometry

The link to the report in PDF is this.

It is highly recommended that the reader have some understanding of measure theory and probability theory before reading.
Sections 4 onwards assume a knowledge of discrete Markov chains (a more general theory of Markov chains is required from section 4.4 onwards, but we give the necessary definitions). A wonderful introduction to both of these is (the first few sections of) Markov Chains and Mixing Times by Levin, Peres, and Wilmer.
Sections 5.2 onwards require a basic knowledge of martingale theory and stochastic calculus, a brief overview of which can be found here. A far better reference for martingale theory is Probability with Martingales by David Williams.

I primarily referred to

• "An Elementary Introduction to Modern Convex Geometry" by Keith Ball for sections 1 through 3,
• "Lectures on Discrete Geometry" by Jiří Matoušek for most of section 3.2 and several scattered parts in sections 1 through 3,
• "How to compute the volume in high dimension?" by Miklós Simonovits and several referenced papers for sections 4.1 and 4.2,
• "Volume Estimates and Rapid mixing" by Béla Bollobás and several referenced papers for sections 4.2 and 4.3,

and many referenced papers from section 4.3 onwards.