From multiplicative unitaries to quantum groups

An alternative version of the theory of multiplicative unitaries is presented. Instead of the original regularity condition of Baaj and Skandalis we formulate another condition selecting manageable multiplicative unitaries. The manageability is the property of multiplicative unitaries coming from the quantum group theory. For manageable multiplicative unitaries we reproduce all the essential results of the original paper of Baaj and Skandalis and much more. In particular the existence of the antipode and its polar decomposition is shown.