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The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems, and letters have spawned a remarkable number of later results by many different mathematicians. Here, his 37 published papers, most of his first two and last letters to Hardy, the famous 58 problems submitted to the Journal of the Indian Mathematical Society, and the commentary of the original editors (Hardy, Seshu Aiyar and Wilson) are reprinted again, after having been unavailable for some time.

In this printing of Ramanujan''s collected papers, Bruce Berndt provides an annotated guide to Ramanujan''s work and to the mathematics it inspired over the last three-quarters of a century. The historical development of ideas is traced in the commentary and by citations to the copious references. The editor has done the mathematical world a tremendous service that few others would be qualified to do.

G. H. Hardy, P. V. Seshu Aiyar, and B. M. Wilson

Some properties of Bernoulli's numbers
On Question 330 of Prof. Sanjana
Note on a set of simultaneous equations
Irregular numbers
Squaring the circle
Modular equations and approximations to ?
On the integral ? ^x₀tan^-1t/t d t

On the number of divisors of a number
On the sum of the square roots of the first n natural numbers
On the product ? ⁿ⁼⁸_n=0[1+(x/a+nd)³]
Some definite integrals
Some definite integrals connected with Gauss's sums
Summation of a certain series
New expressions for Riemann's functions ? (s) and ?(t)
Highly composite numbers
On certain infinite series
Some formulæ in the analytic theory of numbers
On certain arithmetical functions
A series for Euler's constant ?
On the expression of a number in the form ax²+by²+cz²+du²
On certain trigonometrical sums and their applications in the theory of numbers
Some definite integrals
Some definite integrals
A proof of Bertrand's postulate
Some properties of p(n), the number of partitions of n
Proof of certain identities in combinatory analysis
A class of definite integrals
Congruence properties of partitions
Algebraic relations between certain infinite products
Congruence properties of partitions
Une formule asymptotique pour le nombre des partitions de n
Proof that almost all numbers n are composed of about log log n prime factors
Asymptotic formulæ in combinatory analysis
Asymptotic formulæ for the distribution of integers of various types
The normal number of prime factors of a number n
Asymptotic formulæ in combinatory analysis
On the coefficients in the expansions of certain modular functions
Questions and solutions
Appendix I: Notes on the papers
Appendix II: Further extracts from Ramanujan's letters to G. H. Hardy
Commentary on Ramanujan's collected papers