One of the great mysteries of contemporary science is dark matter, an exotic substance of unknown nature that, in theory, makes up about 27% of the total mass-energy density of the Universe, and which does not appear to emit, absorb, or reflect any kind of light, meaning that it is invisible and can only be detected through its gravitational effects on objects around it. Dark matter is a frontier topic, involving highly complex subjects that usually exceed the training of a physics teacher. Given this difficulty, the aim of this paper is to shed some light on dark matter, and to offer a broad, up-to-date introduction that is mainly directed at physics teachers in training and in practice. Due to the breadth of the subject, the article has been divided into two parts. In Part I, we deal with general concepts, which serve as an introduction to the more specific topics analysed in Part II.