The ubiquity and importance of mathematics in our complex society is generally not in doubt. However, even a scientifically interested layperson would be hard pressed to point out aspects of our society where contemporary mathematical research is essential. The way mathematics comes into play in finance, engineering, weather and industry is widely unknown by the public. And who thinks of application fields such as biology, encryption, architecture, or voting systems? This volume comprises a number of success stories of mathematics in our society—important areas being shaped by cutting-edge mathematical research. The authors are eminent mathematicians with a strong talent for public presentation, addressing scientifically interested laypersons as well as professionals in mathematics and its application disciplines.