Set theory and Foundations of Mathematics1. First foundations of mathematicsThe last updated version is as the below list of separate html pages and also all in 1 html page.Previous versions in PDF (13 pages for main text + 7 pages for philosophical aspects). 

1.1. Introduction
to the foundations of mathematics
Mathematics and theories
1.2. Variables,
sets, functions and operations Foundations and developments The cycle of foundations Constants
Free and bound variables Ranges and sets Functions Operations 
Philosophical
aspects
(Each subsection assumes those on its left and top) Intuitive representation and abstraction
Platonism vs Formalism 
1.3. Form of theories
The variability of the model
Notions and objects Onemodel theory On the diversity of formalisms Examples of notions from various theories Metaobjects Components of theories Settheoretical interpretation 
Realistic vs. axiomatic theories in
mathematics and other sciences 
1.4. Structures of mathematical systems
Structures Structures of set theory About of ZF set theory Types in onemodel theory The notion of structure in onemodel theory  
1.5. Expressions and definable structures
Terms and formulas
Variable structures Structures defined by expressions Invariant structures 
Time in model theory
The time of
interpretation
The metaphor of the usual time The finite time between expressions 
1.6. Logical connectives
Negation
1.7. Classes in set
theory Conjunctions, disjunctions Implication Chains of implications and equivalences Axioms of equality Provability The unified framework of theories
Classes, sets and metasets 
The infinite time between theories
Zeno's Paradox 
Definiteness classes 1.8. Binders in set theoryExtended definiteness The syntax of
binders
Definition of functions by terms Relations and setbuilder symbol Russell's Paradox 
Time in set theory
The expansion of the set
theoretical universe
Can a set contain itself ? 
1.9. Quantifiers
The quantifiers ∃,∀
Inclusion between classes Rules of proofs for quantifiers Status of open quantifiers in set theory 
The relative sense of open quantifiers
Interpretation
of classesClasses in an expanding universe
Concrete examples 
1.10. Formalization
of set theory
The inclusion predicate
1.11. Set
generation principle
Translating the definer into firstorder logic First axioms A general principle for the formalization of set theory Formalization of operations and currying Criterion to accept some classes as sets :
Subsets, union, image, ⌀, pairs 
Justifying the set
generation principle Concepts of truth in mathematics Provability
Arithmetic truths Set theoretical truths Alternative logical frameworks 
Other languages :
FR : Théorie des ensembles et fondement des mathématiques : Premiers fondements