Pierre-Simon Laplace (1749-1827) is remembered amoung probabilitists today particularly for his "Theorie analytique des probabilites", published in 1812. This is a thorough and modern translation based on the recent re-issue, with its voluminous notes, of the fifth edition of 1826, with preface by Rene Thom and postscript by Bernard Bru. In the second part of the book, the reader is provided with an extensive commentary by the translator including valuable histographical and mathematical remarks and various proofs.