Kingdom Hearts II/Synthesis

Basics
Synthesis is the making of equipment from two or more materials. This can be done at any Moogle by selecting the "Synthesis" option in the menu. However, Moogle have various ranks (from 1-9), and until they increase in level (by synthesising items), you won't be able to do many of the more advance options, such as creating Mythril Gems.

List of Materials
All of the materials in the game are broken down into shards/stones/gems/crysals and are ranked accordingly. Shards-C Rank Stone-B Rank Gem-A rank Crystal-S rank. The only exceptions are the Orichalcum-A rank and the Orichalcum+-S Rank