This book pays tribute to two pioneers in the field of Mathematical physics, Jiri Patera and Pavel Winternitz of the CRM. Each has contributed more than forty years to the subject of mathematical physics, particularly to the study of algebraic methods.

Self-Similarities and Invariant Densities for Model Sets.- Symmetry Operations in the Brain: Music and Reasoning.- Lie Modules of Bounded Multiplicities.- Moving Frames and Coframes.- The Fibonacci-Deformed Harmonic Oscillator.- Continuous and Discrete Linearizable Systems: The Riccati saga.- Superintegrability on Two-Dimensional Complex Euclidean Space.- Hydrodynamic Systems and the Higher-Dimensional Laplace Transformations of Cartan Submanifolds.- Branching Rules and Weight Multiplicities for Simple and Affine Lie Algebras.- Conditions for the Existence of Higher Symmetries and Nonlinear Evolutionary Equations on the Lattice.- Complete Description of the Voronoi Cell of the Lie Algebra Aäsub nü Weight Lattice. On the Bounds for the number of d-faces of the n-dimensional Voronoi Cells.- The Relativistic Oscillator and the Mass spectra of Baryons.- Seiberg-Witten Theory Without Tears.- Bargmann Representation for Some Deformed Harmonic Oscillators with non-Fock Representation.- The Vector-Coherent State Inducing Construction for Clebsch-Gordon Coefficients.- Higest-Weight Representations of Borcheds algebras.- Graded Contractions of Lie Algebras of Physical Interest.