The Thaumonomicon is a dense tome of arcane and alchemical knowledge, both acquired and yet-to-be-acquired. Whenever Research is successfully completed, and the resulting discovery used, the information learned is added to this book. The Thaumonomicon is the single most important tool a player will create for themselves in ThaumCraft, and (should) last right up until the end of the game. Not only is it the repository for all of the player's completed research, it contains hints for progressing towards more advanced research. Research can be difficult to use, however, because you do not see what elemental propeties are needed, so you are forced to use trial and error.
This item is available both in Thaumcraft 3 and 4.
Crafting the Thaumonomicon is unlike anything else a player may have encountered in Minecraft before, but even still, it is extremely simple to do. First, the player must acquire a conventional Bookshelf (BiblioCraft Bookcases do not work) and place it somewhere in the field. After that, it's as simple as right-clicking it with your Wand to condense the knowledge of the books contained within into your personal magical handbook. (In Thaumcraft 4, you do that with the basic Iron Capped Wooden Wand instead.)
The Thaumonomicon is the basis of all research you will do. It gives, upon a right-click, a complete list in the 'achievement' style of all things which are researchable to the player in an untranslated rune string from the Enchantment table style - an old type of alphabet from a space game called Commander Keen, dating back to 1990s. They are translatable, however. You just need to know them off by heart, or search them under the Standard Intergalactic Alphabet. Keep in mind that you can see elemental properties of an item by shift-clicking it, and you can easily remember eventually how to make certain things, such as Nitor or Alumentum, the two most basic elements you will discover. The Thaumonomicon is important in every Thaumaturge's study, as it is required for almost every research you do.
The Thaumonomicon shows all the Research completed by the player and a few extra things such as a few starting Research pages and some unlockable Research. (The Thaumonomicon hides most of the Research, however; you'll just have to research them to be able to see them!) The Thaumonomicon's lock/unlock status of the research is the same as the vanilla achievements board/list.