This review provides a pedagogical introduction to the eigenstate thermalization hypothesis (ETH) and its implications for statistical mechanics and thermodynamics. The first part of the review introduces ETH as an extension of ideas from quantum chaos and random matrix theory (RMT). It covers classical and quantum chaos, RMT, and the statistics of energy levels, eigenstate components, and matrix elements of observables. The ETH is then introduced, showing how it describes thermalization in isolated chaotic systems without invoking an external bath. Numerical evidence from many-body lattice systems and the concept of quantum quenches are discussed. The second part explores the implications of quantum chaos and ETH on thermodynamics. It derives basic thermodynamic relations, including the second law of thermodynamics, the fundamental thermodynamic relation, fluctuation theorems, the fluctuation-dissipation relation, and the Einstein and Onsager relations. The review shows that quantum chaos allows these relations to be proven for individual Hamiltonian eigenstates, extending them to arbitrary stationary statistical ensembles. It also discusses how these relations can be used to obtain nontrivial universal energy distributions in continuously driven systems. Finally, the review touches on the relaxation dynamics and description after relaxation of integrable quantum systems, where ETH is violated. It introduces the generalized Gibbs ensemble (GGE) and discusses its connection to prethermalization in weakly interacting systems.This review provides a pedagogical introduction to the eigenstate thermalization hypothesis (ETH) and its implications for statistical mechanics and thermodynamics. The first part of the review introduces ETH as an extension of ideas from quantum chaos and random matrix theory (RMT). It covers classical and quantum chaos, RMT, and the statistics of energy levels, eigenstate components, and matrix elements of observables. The ETH is then introduced, showing how it describes thermalization in isolated chaotic systems without invoking an external bath. Numerical evidence from many-body lattice systems and the concept of quantum quenches are discussed. The second part explores the implications of quantum chaos and ETH on thermodynamics. It derives basic thermodynamic relations, including the second law of thermodynamics, the fundamental thermodynamic relation, fluctuation theorems, the fluctuation-dissipation relation, and the Einstein and Onsager relations. The review shows that quantum chaos allows these relations to be proven for individual Hamiltonian eigenstates, extending them to arbitrary stationary statistical ensembles. It also discusses how these relations can be used to obtain nontrivial universal energy distributions in continuously driven systems. Finally, the review touches on the relaxation dynamics and description after relaxation of integrable quantum systems, where ETH is violated. It introduces the generalized Gibbs ensemble (GGE) and discusses its connection to prethermalization in weakly interacting systems.