I.Contents：
Part One, Linear Algebra: Orthogonal matrices, Bilinear forms, The spectral theorem.
Part Two, Groups: The Sylow Theorem, Generators and relations, The Todd-Coxeter Algorithm, The group of motions of the plane, Finite subgroups of the rotation group, The classical linear groups, The Lie algebra.
Part Three, Rings: Maximal and prime ideals, Algebraic geometry, Algebraic integers, Ideal factorization, Some Diophantine Equations.
Part Four, Fields: Constructions with Ruler and compass, Finite fields, Function fields, The main theorem of Galois theory, primitive elements, Kummer extensions, Cyclotomic extensions.
Part Five, Modules: Diagonalization of integer matrices, The structure theorem for abelian groups, Application to linear operators.
Part Six, Group representations: Permutation representations, Regular representations, Unitary representations, Characters, Schur lemma, Orthogonality Relations.
Part Seven, Other topics:
II.Course prerequisite：
Introduction to Algebra (I) (II)
III.Reference material ( textbook(s) )：
Michael Artin, Algebra. Prentice-Hall International, Inc. 1991.
IV.Grading scheme：
(1)Midterm Examination, 40%,
(2) Final Examination, 40%,
(3) Exercises, 20%.
V.Others：