This text is mainly composed of contributions in several former books of the author, which are discussed more detailed here. As the title points up, the aim is the search for structures of primes and their relations to Goldbach's Conjecture, which says that always (odd) primes PI and P2 exist which are solutions to the Diophantine Equation 2n = PI +P2 with natural numbers n>2.In this text, you can find in 8 chapters, after an introduction, special cases of Goldbach's Conjecture, basic formulae of primes, factorial numbers, structures of composite numbers and Goldbach's Conjecture, characteristics of equal sums of primes or composite numbers, the sequence of primes I or II, and additional strategies of proofs.