Modeling the Direct Transition to Turbulence -- Dynamical Systems and the Transition to Turbulence -- Nonlinear Solutions of Simple Plane Shear Layers with and without a System Rotation -- Co-Supporting Cycle: Sustaining Mechanism of Large-Scale Structures and Near-Wall Structures in Channel Flow Turbulence -- Transition Threshold and the Self-Sustaining Process -- Turbulent-Laminar Patterns in Plane Couette Flow -- Subcritical Turbulent Transition in Rotating and Curved Shear Flows -- The Karhunen-Loève Decomposition of the Autonomous Minimal Flow Unit -- Coherent States in Transitional Pipe Flow -- Instability, Transition and Turbulence in Plane Couette Flow with System Rotation -- Transition to Versus from Turbulence in Subcritical Couette Flows -- Transition to Turbulence in Pipe Flow -- Threshold Amplitudes in Subcritical Shear Flows -- Non-Linear Optimal Perturbations in Subcritical Instabilities -- A Bypass Scenario of Laminarturbulent Transition in the Wind-Driven Free-Surface Boundary Layer -- Viscoelastic Nonlinear Traveling Waves and Drag Reduction in Plane Poiseuille Flow -- Subcritical Instabilities in Plane Couette Flow of Visco-Elastic Fluids.An exciting new direction in hydrodynamic stability theory and the transition to turbulence is concerned with the role of disconnected states or finite amplitude solutions in the evolution of disorder in fluid flows. This volume contains refereed papers presented at the IUTAM/LMS sponsored symposium on "Non-Uniqueness of Solutions to the Navier-Stokes equations and their Connection with Laminar-Turbulent Transition" held in Bristol 2004. Theoreticians and experimentalists gathered to discuss developments in understanding both the onset and collapse of disordered motion in shear flows such as those found in pipes and channels. The central objective of the symposium was to discuss the increasing amount of experimental and numerical evidence for finite amplitude solutions to the Navier-Stokes equations and to set the work into a modern theoretical context. The participants included many of the leading authorities in the subject and this volume captures much of the flavour of the resulting stimulating and lively discussions.