- Bureaucracy
- A brief history
- Syntax, semantics, and intended interpretation
- An infinite variety of logics
- Foundational issues
- Soundness and completeness

- Induction
- Formulae: syntax and intended interpretation
- Natural deduction
- Examples of derivation
- Truth tables
- Interdependence of connectives
- Soundness with respect to truth tables
- Boolean algebras
- Semantics and Boolean algebras
- Soundness with respect to Boolean algebras
- Completeness with respect to Boolean algebras

- Signatures, terms, and formulae
- Substitution
- Formal definitions
- Natural deduction
- Examples of derivations
- Tarski’s semantics
- Examples of interpretations
- Soundness
- Completeness
- Compactness
- Examples about compactness
- Löwenheim–Skolem theorem
- Topological interpretation of compactness
- An alternative notion of completeness

- Language
- Paradoxes
- Comparing sets
- Examples of set comparison
- Axioms
- Ordinals
- Transfinite induction
- Ordinal arithmetic
- More on well orders
- Cardinals
- Cardinal arithmetic
- Hierarchy of cardinals
- Axiom of choice
- Continuum hypothesis
- What is a set?

- Computable functions
- Primitive recursive functions
- Examples of primitive recursive functions
- Partial recursive functions
- Enumeration
- Universal function and fixed points
- Pure λ-calculus
- Representable functions in the λ-calculus
- Simple theory of types
- Strong normalisation of the simple theory of types

- Motivation
- Syntax and natural deduction
- Expressive power
- Heyting algebras
- Semantics
- Soundness
- Completeness
- Semantics of first-order intuitionistic logic
- Propositions as types
- Variations on the theme
- Normalisation

- Peano arithmetic
- Standard and non-standard models
- A discussion about limiting results
- Representable entities
- Coding Peano arithmetic into itself
- Fixed point lemma
- Gödel’s first incompleteness theorem
- Gödel’s second incompleteness theorem
- Mathematical meaning of incompleteness
- Natural incompleteness
- Incompleteness in set theory