Quantum semigroups: A survey

Notes of a 8h course given at the University of G"oteborg during an Erasmus exchange visit, June 11-15, 2018. It is intended for PhD and graduate students familiar with $C^{\ast }$-algebras but not specializing in quantum groups. The proofs, if included, are presented in detail, but most facts are not proved. A special emphasis is put onto motivation of the theory and the intuition behind.