List of order-theory notes:

• Well-ordering
• Szpilrajn Extension Theorem
• Zorn's Lemma
• Well-Ordering Principle
• Definability in total orders
• Theories of order
• Ordinal number
• Chajoth's Theorem
• Operations on ordinals
• Limits of ordinals
• Prime components of ordinals
• Divisors of ordinals
• Intermediate value property
• Condensation
• Linear order with successor
• Interval of an ordering
• Order type
• Transitive order type
• Morphisms between linear orders
• Lindenbaum Order-Embedding Theorem
• Preorder
• Galois connection
• Separable order type
• Order type of the irrationals