These book consists of two parts:(i) A detailed introduction by the editor to provide a full exposition on the developments of the study of Goldbach conjecture, including a complete reference.(ii) A collection of original papers on Goldbach Conjecture and is intended for graduate students and researchers in analytic number theory who have an understanding of basic elementary number theory and the theory of the distribution of prime numbers. The basic methods for treating Goldbach Conjecture are the circle method of Hardy and Littlewood and the sieve method of Brun. This book contains papers with originalities and important progresses on these two methods and all the papers in Chinese, French, German and Russian have been translated into English.Contents: Introduction (Wang Yuan)Some Problems of 'Partitio Numerorum'III: On the Expression of a Number as a Sum of Primes (G H Hardy et al.)Representation of an Odd Number as a Sum of Three Primes (I M Vinogradov)A New Proof of the Goldbach-Vinogradov Theorem (Ju V Linnik)A New Proof on the Three Primes Theorem (Pan Cheng Biao)An Elementary Method in Prime Number Theory (R C Vaughan)The Sieve of Eratosthenes and the Theorem of Goldbach (Viggo Brun)New Improvements in the Method of the Sieve of Eratosthenes (A A Buchstab)On Prime Divisors of Polynomials (P Kuhn)On an Elementary Method in the Theory of Primes (A Selberg)On the Representation of Large Even Number as a Sum of Two Almost Primes (Wang Yuan)On the Representation of an Even Number as the Sum of a Prime and an Almost Prime (A Renyi)On the Representation of Large Integer as a Sum of a Prime and an Almost Prime (Wang Yuan)On Representation of Large Even Number as the Sum of a Prime and an Almost Prime (Pan Cheng Dong)The “Density” of the Zeros and Dirichlet L-Series and the Problem of the Sum of Primes and “Near Primes” (M-B Barban)The Density Hypothesis for Dirichlet L-Series (A I Vinogradov)On the Large Sieve (E Bombieri)On the Representation of a Large Even Integer as the Sum of a Prime and the Product of at Most Two Primes (Chen Jing Run)A New Mean Value Theorem and Its Applications (Pan Cheng Dong)Readership: Mathematicians.Key Features: Consists of thousands of pages of articles written by internationally recognized experts in the field along with thousands of relevant literature citations Biological and medical relevance of porphyrins is linked to their chemical, physical and structural features Vast array of information on porphyrin science consolidated into an up-to-date multi-volume series of clear and concise coverage, including hundreds of figures, tables and structural formulas Of interest to chemists, physicists, material scientists, polymer scientists, spectroscopists, electrochemists, electronics and photonics engineers, biochemists, biophysicists, medicinal chemists and clinicians