Lectures on Symmetries provides an elementary introduction to the symmetries of plane figures and platonic solids keeping the prerequisite minimum. The symmetry of an object (in an Euclidean space) is measured in terms of its group of symmetries, which is a subgroup of the group of isometries of the Euclidean space. The primary focus of this book is on transformations of the plane, which helps in deeper understanding of geometry of plane objects. The approach used to understand various concepts is concrete and numerous diagrams are given for better explanation. This book also provides an elementary introduction to Group theory and Linear algebra. The book is a suitable text for an undergraduate course on Groups and Symmetries.

• • All the basic notions of Matrix theory and Group theory are given • The group of isometries of Euclidean Plane is described • Isometries of Wall paper patterns are described with the help of various examples • Rotational symmetries of all the five regular solids are described • The solutions to all the problems are given at the end.

Preface / Theory of Matrices: Definition and Examples / Operations on Matrices / Elementary Row Operations and Row Reduction / Vector Space Rn / Invertible Matrices / Determinant of a Matrix / Permutation Matrices / Eigenvalues, Eigenvectors and Diagonalization / Exercises / Groups: Definition and Examples / Group Homomorphism / Permutation Groups / Cosets of a subgroup / Quotient Groups / Group Actions and its Applications / Structure of Finite Abelian Groups / Exercises / Symmetry: Isometry / Orientations / Composition of Isometries / Group of Isometries of Plane / Group of Symmetries of regular solids / Wall-paper Patterns and Symmetries / Exercises / Solution to Exercises / Bibliography / Index.

Undergraduate and Postgraduate Students