Title: Introduction to quantum information and quantum computing, and non-Markovian dynamics of quantum systems Abstract: Quantum information and quantum computing have become the essential ingredient in many theoretical and experimental studies of quantum mechanics. It provides a topic for multi-disciplinary studies involving also mathematicians, computer scientists and chemists. In this first part of my talk I shall review some basic concepts of the field, with a special emphasis on quantum computing. In the second part I shall concentrate on decoherence phenomena that play a key role - or an obstacle - in successful operation of the quantum devices. The special topic is non-Markovian dynamics that can occur for systems coupled to a structured reservoir, and their modelling.