This book familiarizes the mathematical community with an analytic tool that is capable of so many applications and presents a list of open problems which might be amenable to analysis with order stars.
1. Introduction 2. General order stars 3. Rational approximants to the exponential 4. A-acceptability barriers 5. Multistep methods 6. The advection equation 7. The diffusion equation 8. Pade approximants 9. Contractive approximation 10. Open problems