A Bit of History and Context.- Penning Trap Concept and Implementation.- Hyperbolic and Cylindrical Penning Traps.- Variations on the Penning Trap Concept.- Motion of a Single Particle in an Idealised Trap.- Motion of a Single Particle in a Real Penning Trap.- Inherent Effects of Single-Particle Confinement.- Particle Ensembles in Penning Traps.

- Loading a Trap with Particles.- Excitation of Particle Motions.- Resonant Motional Coupling.- Motional Cooling in Penning Traps.- Particle Ensemble Density: Rotating Wall.- The Concept of Image Charges.- Electronic Detection and Frequency Measurement.- Radio-Frequency Spectroscopy: Penning-Trap Mass Spectroscopy.

- Radio-Frequency Spectroscopy: Outreach.- Optical Spectroscopy.- Laser-Microwave Double-Resonance Spectroscopy.- Magnetic Bottles as Implemented in Penning Traps.- Application of the Continuous Stern Gerlach Effect.- A: Penning Trap Confinement: The Brief Version.- B: Magnetic Field Creation and Control.- C: Equivalence of Results for Magnetic Bottle Strength.

- D: Cryogenics.- E: Collisional Effects in Penning Traps.- F: General Design Considerations.- G: A More Detailed Look at the Potential.- H: A Special Case of Mediated Cooling.