Lecture
1: Introduction
to the Homeomorphism Problem.
This lecture
introduces the basic structure theorems for 3manifolds (Prime Decomposition,
JSJ Decomposition and Thurston's Geometrization Conjecture) and outlines
the solution to the Homeomorphism Problem (and Classification) for
3 manifolds. 

Lecture
2: On
Classifying Manifolds.
This lecture
gives a slightly new approach to the classification of 2manifolds
and a new proof of the topological invariance of Euler characteristic
for 2manifolds; we discuss difficulties of extending these methods
to the classification of 3manifolds; and show the impossibility of
classifying nmanifolds for larger than 3. 

Lectures
3 and 4: Presentations
of 3manifolds.
These
two lectures explore various presentations of 3manifolds via triangulations,
celldecompositions, handledecompositions, Heegaard splittings Heegaard
diagrams, and knot and link projections. Algorithms are given that
transform each of these presentations into a triangulation. 

Lecture
5: Normal
Surface Theory: A Brief Survey.
This lecture
gives a basic introduction to the theory of normal surfaces and establish
some of the fundamental existence theorems. 

Lecture
6: Normal
Surface Theory: Parameterizations
and Algorithms.
This lecture
explores some of the applications ofnormal surfaces to decision problems
in 3manifold topology. 

Lecture
7: Prime
Decomposition of 3manifolds.
This lecture
provides the existence and uniqueness theorems of H.Kneser and J.Milnor
for the prime decomposition of a 3manifolds. 

Lecture
8: An
Algorithm to Construct the Prime Decomposition of a 3manifold.
This lecture
uses the new methods of 0efficient triangulations to give an algorithm
for constructing the prime decomposition of a 3manifold. 

Lecture
9: JSJ
Decomposition of 3manifolds.
This
lectures gives a brief introduction to Seifert fibered 3manifolds
and provides the existence and uniqueness theorem of JacoShalen and
Johannson for the JSJ Decomposition of a 3manifold. 

Lecture
10: An
Algorithm to Construct the JSJ Decomposition of a 3manifold.
An
algorithm is given for constructing the JSJdecomposition of a 3manifold
and deriving the Seifert invariants of the Characteristic submanifold. 

Lecture
11: The
Geometrization Conjecture.
This
lecture discusses the Geometrization Conjecture, the eight locally
homogeneous geometries for 3manifolds and Perelman's Claim of a solution
to the Geometrization Conjecture and its implications. 

Lecture
12: The
Homeomorphism Problem for Haken and Hyperbolic 3manifolds.
This
lecture outlines the solution of the Homeomorphism Problem for Haken
3manifolds and discusses Sela's solution of the Homeomorphism Problem
for closed hyperbolic 3manifolds. 
