Homological algebra provides an indispensable toolbox in the study of the representation theory of algebras. At the heart of this theory, one finds certain fundamental classes of three-term sequences, namely short exact sequences and distinguished triangles. This mini-course gives an introduction to a higher analogue of classical homological algebra that has emerged as a very active area of research over the past two decades. In higher homological algebra, classes of (𝑑 + 2)-term sequences are the key players, where the case 𝑑 = 1 recovers the short exact sequences and distinguished triangles from the classical setup. In particular, the integer 𝑑 ≥ 1 counts the number of middle terms in the distinguished sequences. The mini-course is intended to be accessible to anyone with basic knowledge in representation theory and homological algebra.