Large and Small Polarons -- Optical Properties of Few and Many Fröhlich Polarons from 3D to 0D -- Small Polarons: Transport Phenomena -- Magnetic and Spin Effects in Small Polaron Hopping -- Single Polaron Properties in Different Electron Phonon Models -- Path Integrals in the Physics of Lattice Polarons -- Path Integral Methods in the Su-Schrieffer-Heeger Polaron Problem -- Bipolarons in Multi-Polaron Systems -- Superconducting Polarons and Bipolarons -- Small Adiabatic Polarons and Bipolarons -- From Single Polaron to Short Scale Phase Separation -- Strongly Correlated Polarons -- Numerical Solution of the Holstein Polaron Problem -- Lang-Firsov Approaches to Polaron Physics: From Variational Methods to Unbiased Quantum Monte Carlo Simulations -- Spectroscopic Properties of Polarons in Strongly Correlated Systems by Exact Diagrammatic Monte Carlo Method -- Polarons in Contemporary Materials -- Photoinduced Polaron Signatures in Infrared Spectroscopy -- Polarons in Colossal Magnetoresistive and High-Temperature Superconducting Materials -- Polaron Effects in High-Temperature Cuprate Superconductors -- Current Rectification, Switching, Polarons, and Defects in Molecular Electronic Devices.