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Mathematics
Vertex Algebras
1. Foundations and Motivation
2. Mathematical Preliminaries
3. Basic Structure of Vertex Algebras
4. Axioms and Fundamental Properties
5. Core Operations and Concepts
6. Fundamental Examples
7. Affine Vertex Algebras
8. Virasoro and Conformal Structure
9. Module Theory and Representations
10. Advanced Constructions
11. Intertwining Operators and Fusion
12. Zhu's Theory
13. Vertex Operator Superalgebras
14. Rationality and Finiteness
15. Moonshine and Connections
16. Computational Aspects
17. Applications and Related Areas
Computational Aspects
Structure Constants
OPE Coefficient Calculations
Fusion Rule Computations
Character Calculations
Modular Data
Computer Algebra Methods
Symbolic Computation
Normal Form Algorithms
Gröbner Basis Methods
Representation Software
Classification Problems
Small Central Charge
Minimal Models
Exceptional Cases
Systematic Approaches
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15. Moonshine and Connections
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17. Applications and Related Areas