This collection of papers and essays is the output of the symposium held in ESI, Vienna, June 2006, which commemorated the 100th anniversary of Boltzmann’s death by collecting some of the most prominent experts in contemporary mathematical physics at this event. From all the great physicists and mathematicians of the 19th century, Boltzmann’s legacy is one of the most influential and inspiring today. His achievements in statistical mechanics, the explanation how macroscopic phenomena can be understood from the laws of microscopic (classical) physics, proved to be a real triumph and a culmination of the 'mechanistic' worldview, the theory whose crucial importance in physics, mathematics and other sciences is even more obvious today. However, Boltzmann's legacy should not be viewed as restricted to classical physics, argues E. Lieb in one of the first chapters “What if Boltzmann had known about quantum mechanics”. In comparison to the spectacular and everlasting success of equilibrium statistical physics, even the very foundations of nonequilibrium theory are still a hot discussion topic today. Contributions written by leading scientists reflect this (G. Gallavotti, J. Lebowitz, D. Ruelle, D. Ornstein, C. Cercignani, C. Villani, H. Spohn, E. Cohen, Ya. Sinai and others). There is also a chapter on computer simulations (Ch. Dellago and H. Posch) and on biology (P. Schuster), reflecting Boltzmann's deep interest in evolution theory. The book is framed by introductory and closing essays discussing Boltzmann's philosophical views (J. Renn) and his personality and life (W. Reiter). In summary, this is a valuable book that vividly and from many sides explains, on the occasion of the anniversary of a great scientific personality, one of the most important paradigms of classical and modern science.