In this paper, we want to give an overview of concepts for terraforming Mars. While writing we always were concerned with our mission statement as follows:
"The paper which we are going to write has the aim to explain the "Terraforming idea" to the man in the street who has no interest in scientific formulas."
Keeping the texts simple enough was not always easy because a basic knowledge about physics and chemistry is needed and useful. But after detailed discussions we always were able to progress and eventually finish this paper. As a general introduction to the idea of terraforming Mars, this work does not include all the different plans and suggestions ever made. We explain the basic principles of some commonly suggested terraforming methods, concentrating on models for changing the atmospherical conditions as a first step in making Mars more habitable for terrestrial life. Some central aspects are presented more detailed and with concrete values, but most of these results are unproved estimations and should just give an idea of the general scales. In addition to this overview of scientific research, we give a short summary of the terraforming process depicted in Kim Stanley Robinson's Mars Trilogy. As an example of a fictional prototype model, it can be compared to realistic evaluations and provide another point of view. At the end, we present our own, different opinions on terraforming Mars with respect to the basic motivations and problems. We hope that after reading this paper everybody will know what terraforming Mars is about and perhaps be able to draw a personal conclusion about the sense of terraforming other planets for mankind.