Translated from French.

Includes bibliographical references (p. 403-405) and index.

1. On real functions -- 2. On infinitely small and infinitely large quantities, and on the continuity of functions. Singular values of functions in various particular cases -- 3. On symmetric functions and alternating functions. The use of these functions for the solution of equations of the first degree in any number of unknowns. On homogeneous functions -- 4. Determination of integer functions, when a certain number of particular values are known. Applications -- 5. Determination of continuous functions of a single variable that satisfy certain conditions -- 6. On convergent and divergent series. Rules for the convergence of series. The summation of several convergent series -- 7. On imaginary expressions and their moduli -- 8. On imaginary functions and variables -- 9. On convergent and divergent imaginary series. Summation of some convergent imaginary series. Notations used to represent imaginary functions that we find by evaluating the sum of such series -- 10. On real or imaginary roots of algebraic equations for which the left-hand side is a rational and integer function of one variable. The solution of equations of this kind by algebra or trigonometry -- 11. Decomposition of rational fractions -- 12. On recurrent series -- Note I. On the theory of positive and negative quantities -- Note II. On formulas that result from the use of the signs > or <, and on the averages among several quantities -- Note III. On the numerical solution of equations -- Note IV. On the expansion of the alternating function (y - x) x (z - x) (z - y) x ... x (v - x) (v - y) (v - z) ... (v - u) -- Note V. On Lagrange's interpolation formula -- Note VI. On figurate numbers -- Note VII. On double series -- Note VIII. On formulas that are used to convert the sines or cosines of multiples of an arc into polynomials, the different terms of which have the ascending powers of the sines or the cosines of the same arc as factors -- Note IX. On products composed of an infinite number of factors.

In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the "Cours d'analyse", to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the "Cours d'analyse". For this translation, the authors have also added commentary, notes, references, and an index.