1. Introduction

    1. Canonical identification

    2. Identification via common rationals

    3. Hybrid of canonical identification and identification via common rationals

    4. Topics of the chapter

  2. Summary of the basic physical ideas

    1. p-Adic mass calculations briefly

    2. p-Adic length scale hypothesis, zero energy ontology, and hierarchy of Planck constants

    3. p-Adic physics and the notion of finite measurement resolution

    4. p-Adic numbers and the analogy of TGD with spin-glass

    5. Life as islands of rational/algebraic numbers in the seas of real and p-adic continua?

    6. p-Adic physics as physics of cognition and intention

  3. p-Adic numbers

    1. Basic properties of p-adic numbers

    2. Algebraic extensions of p-adic numbers

    3. Is e an exceptional transcendental?

    4. p-Adic Numbers and Finite Fields

  4. What is the correspondence between p-adic and real numbers?

    1. Generalization of the number concept

    2. Canonical identification

    3. The interpretation of canonical identification

  5. p-Adic differential and integral calculus

    1. p-Adic differential calculus

    2. p-Adic fractals

    3. p-Adic integral calculus

  6. p-Adic symmetries and Fourier analysis

    1. p-Adic symmetries and generalization of the notion of group

    2. p-Adic Fourier analysis: number theoretical approach

    3. p-Adic Fourier analysis: group theoretical approach

    4. How to define integration, p-adic Fourier analysis and -adic counterarts of geometric objects?

  7. Generalization of Riemann geometry

    1. p-Adic Riemannian geometry depends on cognitive representations

    2. p-Adic imbedding space

    3. Topological condensate as a generalized manifold

  8. Appendix: p-Adic square root function and square root allowing extension of p-adic numbers

    1. p>2 resp. p=2 corresponds to D=4 resp. D=8 dimensional extension

    2. p-Adic square root function for p>2

    3. Convergence radius for square root function

    4. p=2 case