1 Characteristic Polynomial in Several Variables -- 2 Finite Dimensional Group Representations -- 3 Finite Dimensional Lie Algebras -- 4 Projective Spectrum in Banach Algebras -- 5 The C⇤-algebra of the Infinite Dihedral Group -- 6 The Maurer-Cartan Form of Operator Pencils -- 7 Hermitian Metrics on the Resolvent Set -- 8 Compact Operators and Kernel Bundles -- 9 Weak Containment and Amenability -- 10 Self-similarity and Julia Sets -- References.

The main goal of this book is to describe various aspects of the theory of joint spectra for matrices and linear operators. It is suitable for a graduate-level topic course in spectral theory and/or representation theory. The first three chapters can also be adopted for an advanced course in linear algebra. Centered around the concept of projective spectrum, the book presents a coherent treatment of fundamental elements from a wide range of mathematical disciplines, such as complex analysis, complex dynamics, differential geometry, functional analysis, group theory, and Lie algebras. Researchers and students, particularly those who aspire to gain a bigger picture of mathematics, will find this book both informative and resourceful.