Discrete finite and Lie groups : comprehensive group theory in geometry and analysis Publisher’s description: In a self contained and exhaustive work the author covers Group Theory in its multifaceted aspects treating its conceptual foundations in a proper logical order. First discrete and finite group theory that includes the entire chemical physical field of crystallography is developed self consistently followed by the structural theory of Lie Algebras with a complete exposition of the roots and Dynkin diagrams lore. A primary on Fibre Bundles Connections and Gauge fields Riemannian Geometry and the theory of Homogeneous Spaces G H is also included and systematically developed. **Group theory is applied in Physics Chemistry Crystallography and many further fields. **Discrete and continuous groups are relevant for probability theory graph theory in the theory of games and as well in economical and statistical sciences.