Prologue: Aims, Themes, and Motivations -- Prologue: Aims, Themes, and Motivations -- Mathematical Framework: Iterated Relations and Composition -- Dynamics of Relations -- Dynamics of Composed Relations -- Abstract Complexity: Abstraction, Invariance, Attraction -- Abstract Observation of Dynamics -- Invariance, Attraction, Complexity -- Abstract Compositional Analysis of Systems: Dynamics and Computations -- Compositional Analysis of Dynamical Properties -- Case Studies: Compositional Analysis of Dynamics -- Experimental Compositional Analysis of Cellular Automata -- Compositional Analysis of Computational Properties -- Epilogue: Conclusions and Directions for Future Work.