This extended tutorial essay views thermodynamics as an incomplete description of quantum systems with many degrees of freedom. The main goal is to show that the approach to equilibrium - with equilibrium characterized by maximum ignorance about the open system of interest - neither requires that many particles nor is it a precise way of partitioning relevant for the salient features of equilibrium and equilibration. Moreover it is indeed quantum effects that are at work in bringing about universal thermodynamic behaviour of modestly sized open systems. Von Neumann`s concept of entropy thus proves to be much more widely useful than something to be feared, and far beyond truly macroscopic systems in equilibrium.

Background.- Basics of Quantum Mechanics.- Basics of Thermodynamics and Statistics.- Brief Review of Pertinent Concepts.- Equilibrium.- The Program for the Foundation of Thermodynamics.- Outline of the Present Approach.- Dynamics and Averages in Hilbert Space.- Typicality of Observables and States.- System and Environment.- The Typical Reduced State of the System.- Entanglement, Correlations and Local Entropy.- Generic Spectra of Large Systems.- Temperature.- Pressure and Adiabatic Processes.- Quantum Mechanical and Classical State Densities.- Equilibration in Model Systems.- Non-Equilibrium.- Brief Review of Relaxation and Transport Theories.- Projection Operator Techniques and Hilbert Space Average Method.- Finite Systems as Thermostats.- Projective Approach to Dynamical Transport.- Open System Approach to Transport.- Applications and Models.- Purity and Local Entropy in Product Hilbert Space.- Observability of Intensive Variables.- Observability of Extensive Variables.- Quantum Thermodynamic Processes.