This is Volume 2 of the envisaged ten-book series and the fourth work to be released to date. It contains complete transcripts of the letters - the majority were composed in Latin - which Euler exchanged with Johann I Bernoulli and Nikolaus I Bernoulli; full translation of all letters; and also critical, historico scientific commentaries. The present edition is uniquely comprehensive, taking into account all known manuscripts. Central topics are: analysis, differential equations, calculus of variations, mechanics, hydromechanics, hydraulics and theory of planetary motions.