1. Introduction

    1. Hyper-octonions and hyper-quaternions

    2. Number theoretical compactification and M8-H duality

    3. Romantic stuff

    4. Notations

  2. Quaternion and octonion structures and their hyper counterparts

    1. Octonions and quaternions

    2. Hyper-octonions and hyper-quaternions

    3. Basic constraints

    4. How to define hyper-quaternionic and hyper-octonionic structures?

    5. How to end up to quantum TGD from number theory?

    6. p-Adic length scale hypothesis and quaternionic and hyper-quaternionic primes

  3. Quantum TGD in nutshell

    1. Geometric ideas

    2. The notions of imbedding space, 3-surface, and configuration space

    3. The construction of M-matrix

  4. Number theoretic compactification and M8-H duality

    1. Basic idea behind M8-M4× CP2 duality

    2. Hyper-octonionic Pauli "matrices" and the definition of associativity

    3. Are Kähler and spinor structures necessary in M8?

    4. How could one solve associativity/co-associativity conditions?

    5. Quaternionicity at the level of imbedding space quantum numbers

    6. Questions

    7. Summary

  5. Octo-twistors and twistor space

    1. Two manners to twistorialize imbedding space

    2. Octotwistorialization of M8

    3. Octonionicity, SO(1,7), G2, and non-associative Malcev group

    4. Octonionic spinors in M8 and real complexified-quaternionic spinors in H?

    5. What the replacement of SO(7,1) sigma matrices with octonionic sigma matrices could mean?

    6. About the twistorial description of light-likeness in 8-D sense using octonionic spinors

  6. An attempt to understand preferred extremals of Kähler action

    1. What "preferred" could mean?

    2. Basic ideas about preferred extremals

    3. What could be the construction recipe for the preferred extremals assuming CP2= CP2mod?

  7. In what sense TGD could be an integrable theory?

    1. What integrable theories are?

    2. Why TGD could be integrable theory in some sense?

    3. Questions

    4. Could TGD be an integrable theory?

    5. Could quaternion analyticity make sense for the preferred extremals?

    6. Are Euclidian regions of preferred extremals quaternion-Kähler manifolds?