Thermodynamic formalism originated as an approach wihin statistical mechanics in physics, in order to explain, among other things, the changes of aggregation states (phase transitions). It was introduced into dynamical systems and mathematically formalised in the 1970s by the work of Sinai, Ruelle and Bowen, mainly in the context of hyperbolic (and symbolic) systems, and found several applications, including dimension theory and fractal geometry. Gradually, also non-uniformly hyperbolic systems entered the picture, with reappearance of phase transitions. The study thermodynamic properties of interval maps is part of this, and in these lectures I will discuss them in greater detail. Among the topics covered: - Historic context (including the Ising model) - Hyperbolic dynamics and the Grifftih-Ruelle Theorem - Non-uniformly hyperbolic dynamics: Intermittent maps vs Hofbauer potential - Interval dynamics: Collet-Eckmann maps and Feigenbaum maps and everything in between. The lectures will be on graduate level or up.