Groups measure symmetry. No where is this more evident than in the study of symmetry in 2- and 3-dimensional geometric figures. Symmetry, and hence groups, play a key role in the study of crystallogra . . . . .

As the title of this course of lectures suggests, my aim was not a systematic treatment of infinite groups. Instead I have tried to present some of the methods and results that are new and look promis . . . . .

Contents: Representations 1 Representation, Maschke’s theorem and semisimplicity 2 The structure of algebras for which every module is semisimple 3 Characters 4 The construction of modules and cha . . . . .

Contents: Groups; Topological groups; Linear Lie groups; Hopf algebras; Appendices.

An early version of these notes was prepared for use by the participants in the Workshop on Algebra, Geometry and Topology held at the Australian National University, 22 January to 9 February, 1996. T . . . . .

Contents: Introduction; Permutation Groups ; Symmetry Groups in Euclidean Space; Representation Theory; Character Tables; Some compact Lie groups and their representations.

These notes, which are a revision of those handed out during a course taught to first-year graduate students, give a concise introduction to the theory of groups. v2.11. (August 29, 2003)

Contents: Linear and multilinear algebra; Representations of finite groups; Character theory; Some applications to group theory; Some group theory.

Contents: Finite-Dimensional Algebras; Group Characters; Divisibility; Induced Characters; further results; permutations and partitions; the irreducible characters of Sn; The Specht modules; Symmetri . . . . .

Contents: Isometries in 2 dimensions; Groups and symmetry; Isometries in 3 dimensions.

Contents:1. Generalities 2. Lie groups and Lie algebras 3. The unitary groups 4. Representations of the SU(n) groups (and of their algebras)5. The tensor method for unitary groups, and the permutati . . . . .

These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of pre . . . . .

The book provides an introduction into the theory of transformation groups at the level of high-school students and university newcomers. Its chapters about group theory were used a textbook in Higher . . . . .

Contents: Fields and vector spaces; Linear and projective groups; Polarities and forms; Symplectic groups; Unitary groups; Orthogonal groups; Klein correspondence and triality; Further topics; Bibliog . . . . .

This is a web-based text on Group Representation Theory. It begins at the undergraduate level but continues to more advanced topics. An early draft of this book was written in TeXmacs during my sab . . . . .