Table of Contents

Lie Groups I: Introduction and Examples.- Lie Groups II: Differential Geometric Properties.- Lie Groups III: Integration, Convolution, and Fourier Analysis.- Variational Calculus on Lie Groups.- Statistical Mechanics and Ergodic Theory.- Parts Entropy and the Principal Kinematic Formula.- Estimation and Multivariate Analysis in R^n.- Information, Communication, and Group Therapy.- Algebraic and Geometric Coding Theory.- Information Theory on Lie Groups.- Stochastic Processes on Lie Groups.- Locomotion and Perception as Communication over Principal Fiber Bundles; and A Survey of Additional Applications.