is perhaps Mersenne's most influential work. It is one of the earliest comprehensive works on music theory, touching on a wide range of musical concepts, and especially the mathematical relationships involved in music. The work contains the earliest formulation of what has become known as Mersenne's laws, which describe the frequency of oscillation of a stretched string. This frequency is: Inversely proportional to the length of the string (this was known to the ancients; it is usually credited to Pythagoras) Proportional to the square root of the stretching force, and Inversely proportional to the square root of the mass per unit length. The formula for the lowest frequency is where f is the frequency [Hz], L is the length [m], F is the force [N] and μ is the mass per unit length [kg/m]. In this book, Mersenne also introduced several innovative concepts that can be considered the basis of modern reflecting telescopes: Much earlier than Laurent Cassegrain, he found the fundamental arrangement of the two-mirror telescope combination, a concave primary mirror associated with a convex secondary mirror, and discovered the telephoto effect that is critical in reflecting telescopes, although he was far from having understood all the implications of that discovery. Mersenne invented the afocal telescope and the beam compressor that is useful in many multiple-mirror telescope designs. He recognized also that he could correct the spherical aberration of the telescope by using aspherical mirrors and that in the particular case of the afocal arrangement he could do this correction by using two parabolic mirrors, though a hyperboloid is required. Because of criticism that he encountered, especially from Descartes, Mersenne made no attempt to build a telescope of his own. Mersenne is also remembered today thanks to his association with the Mersenne primes. The Mersenne Twister, named for Mersenne primes, is frequently used in computer engineering and in related fields such as cryptography. However, Mersenne was not primarily a mathematician; he wrote about music theory and other subjects. He edited works of Euclid, Apollonius, Archimedes, and other Greek mathematicians. But perhaps his most important contribution to the advance of learning was his extensive correspondence (in Latin) with mathematicians and other scientists in many countries. At a time when the scientific journal had not yet come into being, Mersenne was the centre of a network for exchange of information. It has been argued that Mersenne used his lack of mathematical