PRELIMINARIES
	Sets
	Functions
	Graphs
	Homomorphisms of graphs

CATEGORIES
	Basic definitions
	Functional programming languages as categories
	Mathematical structures as categories
	Categories of sets with structures
	Categories of algebraic structures
	Constructions of categories
	Properties of ogjects and arrows in a category
	Monomorphisms and subobjects
	Other types of arrow

FUNCTORS
	Functors
	Actions
	Types of functors
	Equivalences
	Quotient categories

DIAGRAMS, NATURALITY AND SKETCHES
	Diagrams
	Natural transformations
	Natural transformations between functors
	The Godement calculus of natural transformations
	The Yoneda Lemma and universal elements
	Linear sketches (graphs with diagrams)
	Linear sketches with constants: intial term models	

PRODUCTS AND SUMS
	The product of two objects in a category
	Notation for and properties of products
	Finite products
	Sums
	Natural number objects
	Deduction systems as categories

CARTESIAN CLOSED CATEGORIES
	Cartesian closed categories
	Typed --calculus
	--calculus to category and back
	Arrows versus terms
	Fixed points in cartesian closed categories

FINITE DISCRETE SKETCHES
	Finite Product Sketches
	The sketch for semigroups
	Notation for FP sketches
	Arrows between models of FP sketches
	The theory of an FP sketch
	Initial term models for FP sketches
	Signatures and FP sketches
	FD sketches
	The sketch for fields
	Term algebras for FD sketches

LIMITS AND COLIMITS
	Equalizers
	The general concept of limit
	Pullbacks
	Coequalizers
	Cocones
	More about sums
	Unification as coequalizer

MORE ABOUT SKETCHES
	Finite limit sketches
	Initial term models of FL sketches
	The theory of an FL sketch
	General definition of sketch

THE CATEGORY OF SKETCHES
	Homomorphisms of sketches
	Parametrized data types as pushouts
	The model category functor

FIBRATIONS
	Fibrations
	The Grothendieck construction
	An equivalence of categories
	Wreath products

ADJOINTS
	Free monoids
	Adjoints
	Further topics on adjoints
	Locally cartesian closed categories
	
ALGEBRA FOR ENDOFUNCTORS
	Fixed points for a functor
	Recursive categories
	Triples
	Factorizations of a triple
	Scott domains

TOPOSES
	Definition of topos
	Properties of toposes
	Is a two-elemetn poset complete
	Presheaves
	Sheaves
	Fuzzy sets
	External functors
	The realizability topos

BIBLIOGRAPHY