These lecture notes cover introductory quantum theory to an extend that can be presented in a one semester course. The subject is approached by looking first at some of the pressing questions by the end of the 19th century, when classical physics, in the eyes of many, had come close to explaining all known physical phenomena. We will focus on a special question (e.g. the black body problem), then introduce an idea or concept to answer this question in simple terms (e.g. energy quantization), relate the quantum theoretical answer to classical theory or experiment, and finally progress deeper into the mathematical formalism if it provides a general basis for answering the next question. In this spirit we develop quantum theory by adding in a step by step procedure postulates and abstract concepts, testing the theory as we go along, i.e. we will accept abstract and maybe sometimes counter intuitive concepts as long as they lead to verifiable predictions.